JOURNAL OF GEOPHYSICAL RESEARCH,VOL. 90, NO. B14,PAGES 12,415-12,433,
DECEMBER 10, 1985
The Evolution of Impact Basins'
Cooling, Subsidence,and Thermal Stress
STEVEN R. BRATT! AND SEAN C. SOLOMON
Departmentof Earth, Atmosphericand Planetary Sciences,MassachusettsInstitute of Technolo•7y,Cambrid•7e
JAMES W. HEAD
Departmentof Geolo•7icalSciences,Brown University,Providence,Rhode Island
Potentially important contributors to the topography and tectonicsof multi-ring impact basins are the
thermal contraction and thermal stressthat accompany the loss of heat emplaced during basin formation. Heat converted from impact kinetic energy and contributed from the uplift of isotherms during
cavity collapse are important componentsin the energy budget of a newly-formed basin. That the
subsequentcooling may have been an important factor in the tectonic evolution of the Orientale basin is
suggestedby the deep central depressionand by a surroundingregion of extensivefissuring.To test these
concepts,we develop models for the anomalous temperature distribution immediately following basin
formation, and we calculate the resulting elastic displacement and stressfields that then would accompany cooling of the basin region. All models predict subsidenceof the basin floor and a near-surface
stressfield consistent with fissuring. In addition, the rates of cooling and of accumulation of thermal
stressare in agreementwith the inferred timing of fissureformation in Orientale. The sensitivity of the
predicted displacementsand stressesto the initial temperature field allows us to place bounds on the
quantity and distributionof impact heat emplacedduring basinformation. In order to be consistentwith
the observedtopography and the distribution of fissuresin the Orientale basin, the buried heat deposited
duringthe basin-forming
eventwas between1032and 1033erg. It is likely that most of this heat was
concentrated within a distance of 100-200 km from the point of impact.
INTRODUCTION
Multi-ring impact basins on the Moon exhibit wide variations in their presentgeometryand structure [Hartmann and
Wood, 1971; Wilhelrns,1973; Wood and Head, 1976]. Some of
the variations may be related to differencesin the propertiesof
the lithosphere or impacting projectile at the time of basin
formation [e.g., Melosh and McKinnon, 1978; Holsapple and
Schmidt,1982]. Many of the observedvariations likely reflect
different degreesof modification of initial basin geometry and
structure on time scaleslong compared to those for cavity
excavation and ring formation. The subdued topographic
relief of basinsformed early in lunar history when the lithospherewas relatively warm is probably a consequenceof lateral flow of crustal material over times scales ranging up to
millions of years [Solomon et al., 1982; Bratt et al., 1985a].
The infilling of impact basins with mare basalt, on a somewhat greater time scale,led to loading of the lunar lithosphere
and consequentsubsidenceand flexurally-inducedtectonic activity [Solomonand Head, 1979, 1980; Comeret al., 1979].
Thermal contraction and thermal stressaccompanying the
loss of heat emplaced during basin formation are two additional and potentially important contributors to the longterm modification of an impact basin [Bratt et al., 1981].
During impact a significant fraction of the projectile kinetic
energyis convertedto buried heat [O'Keefe and Ahrens,1976,
1977]. Further, the uplift of lower crustal and upper mantle
material during collapseof the excavatedcavity and formation
•Now at ScienceApplications International Corporation, San
Diego, California.
Copyright 1985 by the American Geophysical Union.
Paper number 5B5451.
0148-0227/85/005B-5451$05.00
of the multi-ring basin [Melosh and McKinnon, 1978] results
in a correspondinguplift of the crustal and mantle isotherms,
an additional source of heat beneath newly formed basins.
Conduction of this anomalous heat to the surfacegivesrise to
lithospheric thermal contraction and stress.
In this paper we assessthe contribution of thermal contraction and thermal stressto the topography and tectonics of
large lunar impact basins.Exploratory models are developed
for the temperature structure following basin formation, for
the subsequentcooling of the basin region, and for the resulting thermal displacementsand stressesas functions of
time. The subsidenceand stressat the surfaceare compared
with topographyand tectonicfeaturesin the comparatively
well-preserved Orientale basin [Head, 1974; Church et al.,
1982]. On the basisof thesecomparisonswe derive approximate constraintson the quantity and distribution of heat implantedduring the basin-formationprocess.
GEOLOGICAL OBSERVATIONS: THE ORIENTALE BASIN
The Orientale basin (Figure 1), the youngestand best preserved of all lunar impact basins [Head, 1974; Moore et al.,
1974], is an important source of information about the formation and modification of impact basins on all the terrestrial
planets. Only the centralmost 220 km of the 900-km-diameter
topographic depressionis extensivelycovered by mare basalt
[Head, i974], leaving exposedmany geologic units and tectonic features that are presumably hidden beneath mare units
in other nearside basins. BecauseOrientale is the youngest
major basin on the Moon [Wilhelms, 1979], it has been left
relatively undisturbed by ejecta deposits from other large
impact events.Orientale is thus a nearly ideal location to look
for tectonic and topographicexpressionsof basin cooling.
A careful documentationof the principal structural features
and morphological units within the Orientale basin has been
made by Church et al. [1982]; see Figure 2. The plains and
12,415
12,416
BRATT ET AL.' THERMAL STRESSNEAR COOLING IMPACT BASINS
Fig. 1. The Orientale basin. The basin center is located near 20øS, 95øW' the diameter of the outer ring (Cordillera
Mountains) is about 900 kin. Lunar Orbiter photograph LO IV-194M.
corrugated facies,which surround and probably underlie the
central mare, are interpreted as cooled impact-melt material
[Head, 1974]. Head [1974] and Church et al. [1982] suggest
that the pitted and cracked texture of the corrugated facies
resultedfrom cooling and internal thermal contractionsacting
duringthe time intervalof melt-sheetcooling,about 103 to
10'• yr [Onoratoet al., 1978]. The outer Rook Mountains,
believed to representthe rim of the original impact cavity,
bound the outer edge of the corrugatedand plains faciesat a
radial distance of about 310 km from the basin center [Head,
1974, 1977].
Mare ridges and arcuate rilles (graben) constitute the innermost and outermost tectonic features,respectively(Figure 2).
Both types of featurespostdatethe emplacementof the central
mare units and are consistentwith the pattern of stressesproduced by lithosphericloading and flexure [Comer et al., 1979;
Solomonand Head, 1980]. No graben such as those found in
Orientale
and other mascon mare basins have been identified
BRATTET AL.' THERMALSTRESS
NEAR COOLINGIMPACTBASINS
12,417
STRUCTURAL
FEATURES
i_
GRABEN•1
=MARE
RIDGES_•PITTED
AND
CRACKED
I FACIES
OUTER
MARE
INNER MARE.d_.
-2
I
I
CORRUGATED
AND
PLAINS
_L.
T
DOMICAL
RADIAL
I
6 CENTRAL
0
•
'"T-
I00
200
ORIENTALE
300
400
500
600
r, krn
Fig. 2. Generalizedtopographicprofile of Orientale, after Head et al. [-1981].The z = 0 datum correspondsto the
typical level of surroundingterrain. Also shown are the locations of ring structures,stratigraphicfacies,and tectonic
features,after Churchet al. [1982].
in the vicinity of farside basins not filled by mare units. It is
therefore unlikely that the rille systemswere formed in responseto basin cooling, a processwhich would be expectedto
affect basinsof a given age and size to a similar extent.
Tectonic features not obviously related to basin formation,
melt-sheet cooling, or mare loading are the narrow fissures
that occur within the corrugatedand plains faciesof Orientale
(Figure 3). Most fissuresare generally concentric to the basin
and are concentrated
in an annular
band between
150 and 230
km from the basin center (Figure 4). In the southern quadrant
of the basin, portions of some of the innermost fissuresare
buried by basaltsof the inner mare (Figure 3), so that fissuring
may have extendedsomewhatinward of 150 km distanceprior
to emplacementof the central mare units. In other quadrants,
however, the corrugated and plains faciesare exposedinward
of 150 km radial distanceand lack extensivefissuring.Neither
Mohr circle approachesthe failure envelope only along the
normal stress axis. Consider, for example, the state of stress
characterizedby Mohr circle a (Figure 5) with diameter a•
- 0.3,where 0.• and 0'3 are the maximum and minimum principal stressesand stressis positive in compression.Mohr circle
a indicates that extensionalfracturesdevelop in diabase when
0'3 reaches -0.4 kbar and when 0'• is less than 1.5 kbar.
Because most fissuresin Orientale are approximately concentric to the basin (Figure 4), 0'3 must have been generally
horizontal
and radial to the basin center at the time of fissure
formation. Further, the magnitude of this radial stressin the
vicinity of these fissuresmust have generally exceededthe extensional strength, approximately 0.2 to 0.4 kbar for competent igneousrocks at low confining pressure[Brace, 1964].
The direction of 0'• may have been either vertical or horizontal (i.e., azimuthal).
vertical nor horizontal offsets are resolvable across individual
Photogeologic observations provide important constraints
fissures,though some component of dip-slip or strike-slip on the timing of fissureformation [Church et al., 1982]. Bemotion cannot be excluded for some of these features. The
causemare basalts flood portions of fissures,the fissuresmust
fissuresdiffer in both geometry and distribution from the predate at least the most recent episode of mare volcanism
graben. Whereas graben have fiat floors up to 4 km in width, within the central basin. In addition, Church et al. [1982]
fissureshave narrow V-shapedcrosssections.The grabentend concludedthat the fissurespostdate the cooling of the corruto occur outward of the zone of most intensefissuring,but the gated and plains facies (impact melt sheet) on which they
innermost graben and outermost fissures overlap in radial formed. One reason for this view is that portions of the corrurange (Figure 4).
gated and plains faciesare not cut by fissures,indicating that
The fissuresare most readily interpreted as extensionfrac- fissuringis the result of processesother than cooling and conturesformed under tensionalhorizontal stressat low confining traction of the melt sheet. On the basis of these relative age
pressure.An understandingof such a stressregime may be relations and estimatesfor the ages of the Orientale impact
obtained from a Mohr failure envelope.In Figure 5 is shown event and of the central mare deposits[Greeley, 1976], Church
the failure envelopederived by Brace [1964] from laboratory et al. [1982] concludedthat the deformation that led to fissure
measurementsof the strengthof Frederick diabaseunder axial formation occurred during a 100 to 200 m.y. time period folextensionand compression.At high confining pressures,the lowing basin formation. They further suggested,on the basis
failure envelopeis defined by straight lines, signifyinga con- of preliminary thermal evolution models for impact basins
stant angle of shear failure. At low confining pressure,how- [Bratt et al., 1981], that the fissureswere principally the result
ever, the envelope bends to intersect the normal-stressaxis at of thermal stress.
a right angle [Gri•t•tsand Handin, 1960; Muehlberger, 1961] to
It has also been proposedthat a portion of the topographic
be consistent with the formation of extension fractures orientrelief of the Orientale basin (Figure 2) may be the result of
ed normal to the direction of greatest extensional stress.Ex- thermal contraction [Bratt et al., 1981; Church et al., 1982].
tension fractures will be favored over shear failure when the
The total relief from the central depressionto the Cordillera
12,418
BRATTET AL.: THERMALSTRESS
NEAR COOLINGIMPACT BASINS
Fig. 3. A portion of the Orientalebasin,showing(top to bottom)inner mare,the corrugatedand plainsfacies,and the
domical faciesof Head [1974] and Church et al. [1982]. A number of fissuresare evident on the corrugatedand plains
units.Lunar Orbiter photographLO IV-195H1; width of imageis 270 km.
Mountains exceeds9 km [Head et al., 1981]. The strongest inner Rook Mountains about 180 km distant is nearly 4 km.
signatureof thermal contractionpostdatingbasinformation is In addition, the central basin region is floored by mare basalts
likely to be concentratedin the centralbasinregion.The topo- up to perhaps 1 km in thickness[Head, 1974]. We regard the
graphic relief between the basin center and the foot of the 5 km of relief from the base of central mare units to the foot of
BRATTETAL.' THERMAL
STRESS
NEARCOOLING
IMPACTBASINS
ORIENTALE
12,419
STRUCTURE
•[-
•"• CORDILLERA
MTNS.
ee
eß
ß
•
ß
i•NNE'R
;
ß
ß
t
ß
/
ß
ß
-.
ß
ß
ß
!
•\•
OUTER
ROOK
MTNS.
Sketchmapof Orientale,showingbasinrings,fissures
(thinlines)and graben(doublehatchedlines).Features
weremappedfromLunarOrbiterphotograph
LO IV-194M (Figure1),a slightlyobliqueview.
Fig. 4.
the inner Rook Mountains as an upper bound on the subsi-
proximatedby a sum of suitablyweightedsolutionsfor uni-
form cylinders.This geometryis illustratedin Figure 6.
The solution for the temperaturefield in a halfspacedue to
Belowwe presentmodelsfor the thermalcontractionand coolingof a buriedcylinderinitially at temperatureTobegins
thermal stressthat accompanycooling of an Orientale-size with the solution for the temperaturein an infinite medium
basin. We use as primary constraintsthe subsidenceof the due to an instantaneoustemperaturechangeTo within a unit
centralbasinregionby asmuchas 5 km and the formationof volume of material located at the origin [Carslaw and Jaeger,
fissuresas times lessthan 200 m.y. after basin formation and 1959]:
denceexperiencedby Orientale as a result of cooling and
thermal
contraction.
at distances of 150 to 230 km from the basin center.
BASIN THERMAL
EVOLUTION
We describe the thermal evolution of an impact basin
To e_tr2+=2•/c2
T(r,z' t)= •3/2c3
(1)
where t is time, c = 2(kt)•/2 and k is thermal diffusivity.We
next apply the methodof imagesto satisfythe boundarycon-
regionwith a simpleanalyticalmodelobeyingcylindricalsym- dition T - 0 at the free surface,and we integrateover a cylinmetry. Let r, 0, and z be the cylindricalcoordinatesradius, drical volume of initial temperature T0. The solution for a
azimuth, and depth. Becauseof linearity we need consider buriedcylinderof uniforminitial temperatureis then
only the anomaloustemperaturefieldbeneatha basin,i.e.,the
temperaturein excess
of the pre-impactthermalgradient.It is
r(r,z' t)= •7
r'e
sufficientto solve the problem of the thermal evolution of a
halfspacein which the initial anomaloustemperatureis uniformly TO within a buried vertical cylinder,extendingfrom
•o
• -,/
•2'c:
/2rr'\
To
e-,.:/c:
Iot•--7-;
dr'
r -- 0 to r -- a and from z -- h• to z - h2, and the temperature
is zero outsidethe cylinder.The solutionfor any cylindrically
symmetricinitial distributionof temperaturemay then be ap-
.Ierf(h27Z)-erf(h'7Z)-erf(h2c
(2)
12,420
BRATT ET AL.' THERMALSTRESSNEAR COOLINGIMPACT BASINS
or, kbar
Fig. 5. Mohr failure envelope for Frederick diabase derived from the laboratory experimentsof Brace [1964]. The
quantities a and ß are normal and shear stress,respectively;a• and a 3 are the greatestand least compressiveprincipal
stresses.
Circle a representsa stressfield capableof producingextensionalfissurestrendingat an angle 0 = 90ø from a 3.
The stressfield correspondingto circle b leadsto shearfailure along faults trending at 0 = _ 66ø from a3.
where err is the error function [Gautschi, 1964] and I o is a
modified Besselfunction [Olver, 1964]. The integral in equation (2) is identical to the P function describedby Masters
[1955]. A thermal evolution model for an impact basin region
follows from (2) and from a specificationof an initial distribution of anomaloustemperature.We defer discussionof the
temperature field immediately following basin formation to a
wherethe thermoelasticdisplacementpotentialsare
c)i=
•
dr'dO'
dz'
(6)
• r'dr'dO'
dz'
(7)
v
(]•2
=
later section.
THERMAL
DISPLACEMENT
are integralsover volume V in the half-space,weightedby the
AND STRESS
inverse of the distance scalars
Differential cooling of an elastic medium will lead to spatially variable thermal contraction and to thermal stress.To
calculate these quantities from a thermal evolution model, we
use the method of thermoelastic displacement potentials
[Goodier, 1937]. During a time interval At, there will be a
non-uniform changein the temperaturefield givenby
AT=
T(r, z ; t) - T(r, z ; t - At)
(3)
R•'- [(r - r')2 - 2rr' cos(0 - 0') + (z -- j,)211/2
(8)
R2'= [(r - r')2 -- 2rr' cos(0 -- 0') + (z + z')2]1/2
(9)
The vector operator applied to &2 is
V2&2
=(3-4v)V&2
+2V[z(O•)]-4(1-v)V2(z&
The response
of an elasticwhole-space
to sucha temperature
(10)
changecan be representedby a distribution of centersof contraction (or dilatation) of magnitude:
r
0•AT(1 + v)
,8= 12•(1
- v)
(4)
where 0•is the volumetriccoefficientof thermal expansionand
v is Poisson's ratio [Goodier, 1937]. The solution for thermal
stressin a halfspacemust satisfythe additional conditionthat
the surface
be free of shear and normal
tractions.
To
meet
these boundary conditions, Mindlin and Cheng [1950] modified the formulation of Goodier[1937] by imposinga centerof
contraction,a double force,and a doublet,eachof appropriate
strength, at the image point (r, -z) correspondingto each
center of contraction (r, z) in the half-space.As a result, the
thermal displacementfield u = (u, v, w) in cylindrical coordinates is given by
U --' -- Vlpl -- V2{P2
(5)
AT:O
Fig. 6. Geometry of the thermoelasticstressproblem for a cooling impact basin. Over each time interval At, cylinders of constant
temperature changeAT can be superposedto form any axisymmetric
distribution of temperaturechange.
BRATTET AL.' THERMALSTRESS
NEAR COOLINGIMPACTBASINS
whereV2 is the scalarLaplacianand ekis the unit vectorin
12,421
• = Ou/Or
(15)
%o= u/r
(16)
the z direction.
By symmetry, we can solve for the displacementfield by
approximating the temperaturechange field AT(r, z; t) by a
set of cylindersof uniform temperaturechange,computingthe
displacements
due to the coolingof individual cylinders,and
then summingthe resultingdisplacementsolutions.The calculation of displacementsfrom (5) reducesto differentiation if
the potential of the distribution of temperature changesis
known. Unfortunately, the solution for the potential surrounding a cylinderdoesnot condenseto a simpleequation.
An expressionfor the potential of an infinitely thin disk of
radius a has been derived by C. H. Thurber (personalcommunication,1980)and is givenby
k=
!)2(2k)!
•b,(r,
z)=2n/•
•o24n(k
(4k)!
F2k
•0
ait,2+r2(2_
r•2k
+Z,)232k+
1 1/2dr'
(12)
which, for r- 0, is simply the potential of a thin disk at a
point on the axis [Moulton, 1914, p. 113]. The number of
terms necessaryto evaluate (11) is a function of the location of
the observation point, (r, z- z') or (r, z + z'), relative to the
disk.
To obtain the potential of a cylinder of finite thicknessand
constant temperaturechange,we numerically integrate equation (11) over z'. The displacementpotential •b2may similarly
be computedby substitutingthe quantity (z + z') for (z - z') in
(11) prior to integration over z'. The displacementfield follows
directly from centered-differencenumerical differentiation of
•bx and •b2as prescribedby (5) and (10).
The accuracyof this method was testedby approximating a
buried sphereby a stackof buried cylinders.We comparedthe
potentials for the two problems,and we also compared the
displacementfield produced by the cooling of the cylinder
stackwith the displacements
at the free surfaceresultingfrom
the cooling of a buried sphere[Mindlin and Cheng,1950]. The
difference between our approximate solution and the exact
solutioncan be made to vanishby using suitably thin cylinders.We are confident,therefore,that the approximationswe
have adopted can adequatelyrepresentthe displacementfield
due to the cooling and contractionassociatedwith any axisymmetricinitial temperaturestructure.
In the models that follow, we examine the displacements
and stressesonly at the lunar surface.Thus, the normal stress
azz, the shear stresses%z and a0z,and the local temperature
changeare all zero. The shear stressarois also zero by symmetry. The thermal stressesat the free surface are calculated
from the displacementfield in (5) using standard formulae
[Timoshenkoand Goodier,1970, p. 456]:
*" = -(1 + v)(1
- 2v)[(1 O'00 •-
(1 + v)(1 - 2v)
(17)
Differentiation in (15) and (17) is accomplishednumerically
usingthe centereddifferencemethod.
The stressesgiven by (13) and (14) are relative to the ambient state of stressat t = 0, immediatelyfollowing basin formation. While we concentratebelow on the time-dependentthermal stressproduced during basin cooling, the possiblemodifyinginfluenceof a non-zeroprestressis alsodiscussed.
ANELASTIC EFFECTS
The equations presentedabove provide a simple procedure
to compute the thermoelastic displacementsand stressesfor
an axisymmetric thermal evolution model. Several uncertainties in the underlying assumptionsare noteworthy. Perhaps least certain is the assumption that the moon behavesas
a conductive, elastic half-spaceduring basin thermal evolution. The thermal model will be valid only if convectivetransport of heat in the shallow sub-basin region is unimportant,
and the stressfield will be correct only if the material undergoing temperature change behavescompletely elastically.It is
(11)
The integration in (11) can be solvedby parts for any given k;
for example,the k - 0 term reducesto
2•r/•[(a2 + r2 + (z - z')2)•/2 - (r2 + (z - z')2)•/2]
•zz = Ow/Oz
v)a. + v(aoo
+ azz)]
(13)
[(1 - v)%o+ v(e,, + ezz)]
(14)
lik.ely,however,that at hightemperatures
stress
will berapidly
relievedby ductile flow. While equations(4)-(10) may still give
a reasonable approximation to the overall displacementfield
for the purpose of estimating subsidenceof the surface,equations (13)-(17) will not give a correct representation of the
thermal stressfield in the presenceof strongly anelasticbehavior. From the depth distribution of intraplate earthquakes,
Chenand Molnar [1983] estimatethat the earth'scrust and
upper mantle display brittle behavior only at temperatures
lessthan 250ø-450øC and 600ø-800øC,respectively.From flexural studies, McNutt and Menard [1982] conclude that the
base of the elasticlithospherebeneath ocean basinsis defined
approximately by the 550øC isotherm. While the lunar thermal profile is highly uncertain, particularly near the time of
major basin formation, the thermal history model of Solomon
and Head [1979] indicatesthat only the upper 25 km of lunar
crust were at temperatures less than 250øC and that little or
none
of the
mantle
was
cooler
than
500øC
at the
time
of
formation of Orientale (about 3.8 b.y. ago). The anomalous
heat emplaced during basin formation further reduces the
volume of subsurfacematerial capable of elastically sustaining
stress.Some caution, of course, should be exercisedin transferring to the moon information on the depth extent of elastic
behavior on the earth. Neither the average time-dependent
lunar temperature profile nor the rheology of the lunar litho-
sphere is well known. Material near the lunar surface undoubtedly cooled rapidly after basin formation, however,even
if mass flow did not contribute significantlyto heat transport.
It is thus likely that the upper lunar crust beganto accumulate
elasticstress(and episodicallyto undergo brittle deformation)
shortly after basin formation as a result of material cooling
and contracting at greater depth.
In the simple models consideredhere, it is not possibleto
examine completely the effects of depth- and temperaturedependent rheology on near-surface displacements and
stresses.To simulate some of the effectsof rapid stressrelaxation in regions of high temperature,however, we may postu-
whereE is Young'smodulus,stressis positivein compression, late that material does not contribute to the thermal stress
strain is positive in extension,and the strain componentsare field until it has cooled below some elastic "blocking tempergiven by
ature" Te I-Turcotte, 1974, 1983' Bratt et al., 1985b]. This pos-
12,422
BRATT ET AL.: THERMALSTRESSNEAR COOLINGIMPACT BASINS
PRE-
IMPACT
CRUST
IMPACT
HEATING
CAVITY
EXCAVATION
•
•
m
I
I
•
ß
',,,,,,,
',.... •,, ,)
CAVITY
ISOTHERM
,"
I
I
I
,,,,,,i
' -,--
I
I
I/
j?
.',',
,•.-•
-,.-.
-..•
t"
COLLAPSE
UPLIFT
Fig. 7. Schematic
viewof thetwo principalsources
of deepheatingthat accompany
basinformation.
tulate can be readilyimplementedinto the proceduredetailed sourcesof heat below, and we derive simple relationshipsfor
aboveby stipulatingthat if eitherT(r, z; t) or T(r, z; t -- At) in the anomaloustemperaturebeneatha newly formedbasin.We
(3) exceedsTe,then that temperatureis set equal to Te.The then apply thesetemperaturedistributionsto investigatethe
deepestnonzerocontourof AT that contributesto thermal contribution of cooling to the topography and tectonicsof
stress at the surface would then follow closely the T = Te
Orientale.
isotherm,and Tecan be regardedas approximatingthe temperatureat the baseof the mechanicallystrongelasticlitho- Impact Heating
sphereof the moon. We includean elasticblockingtemperThe quantity and distribution of heat emplaced during a
ature in a subset of the stress models discussed below. The
hypervelocityimpact, as well as the sizeof the basinremaining
blockingtemperaturehypothesisis usedonly for the calcula- after excavation and short-term modification, are complex
tion of thermal stress.We apply equations(3) and (5) in their functions of the mass, volume, and velocity of the projectile
unmodifiedform to predict basin subsidencein responseto and of the gravity, density, and strength near the planet surface '[e.g., Holsapple and Schmidt,1982]. Given only the observedbasin morphology,it is difficult to estimatethe original
INITIAL THERMAL STRUCTURE
kinetic energy (Es:)of the impacting body. Many of our presThe impact of a basin-formingprojectilewith a planet in- ent conceptionsabout the energeticsand mechanicsof basin
volvesa •ransfer
of projectile
kineticenergyprimarilyto heat- formation follow from scaling of smaller craters formed by
ing of the target area and secondarilyto ejection of some ancient impacts on the earth [Shoemaker,1960; Grieve et al.,
portion of heated target material [e.g., O'Keefe and Ahrens, 1977-],nuclearand chemicalexplosionsin the field [e.g., Vaile,
1976, 1977]. The deep structure of the youngest nearside 1961; Nordyke, 1961, 1977], and impact experimentsin the
basins[Bratt et al., 1985a] suggeststhat the excavatedcavities laboratory [e.g., Gault and Wedekind, 1977; Schmidt,1977].
for basins the size of Orientale penetrated to the lower crust Valuable information on cratering has also been derived from
or upper mantle and that the volumeof ejectedmaterial is on analytical and numericalsimulationsof crater formation [e.g.,
the order of 107 km3. Collapseof the excavatedcavity was Gault and Heitowit, 1963; Maxwell, 1977; O'Keefe and Ahrens,
accomplishedat least partly by uplift of the underlying crust 1976, 1977]. Estimates for the total kinetic energy (Es:) reand upper mantle [Head, 1974; Melosh and McKinnon, 1978]; quired to form an Orientale-sizebasin on the moon, however,
the uplifted material would be hotter than surroundingma- can vary by several orders of magnitude depending on the
terial even in the absence of other effects of the impact. Thus scaling law applied. For instance,assuming that the crater
explosion(yield= 5 x 10TMerg,
immediately after the basin-formingevent, the basin region producedby the Teapot-Ess
was subjectedto two primary sourcesof deep heating(Figure diameter = 89 m [Nordyke, 1961]) is a good terrestrial analog
7): (1) conversion of impact kinetic energy to buried heat of larger impact craters [Shoemaker,1960], the kinetic energy
fooling.
(hereinafterreferred to as impact heating),and (2) uplift of
crustal and mantle isothermsduring collapseof the excavated
cavity (hereinaftertermed isothermuplift). We considerboth
requiredto form Orientalerangesfrom about 103• erg if
Es:•' D3 to 1035 erg if Es:.,. D4 [Holsappleand Schmidt,
1982], where D is the crater diameter.
BRATTET AL.: THERMALSTRESS
NEARCOOLINGIMPACTBASINS
TABLE
1.
Models
of Thermal
Stress for the Orientale
Basin
Buried
Model
Number
A
s, km
Te, øC
.........
Figure
Included? Number(s)
yes
where s is a decay constant (the distance from the center of
symmetry at which heating falls to 1/e of its peak value), p is
density(eithercrustalor mantle),and Cpis specificheat.The
Impact
Decay
Blocking
Uplift
Heat Es, Constant Temperature Heating
1032erg
12,423
latent heat of phase changesis ignored. The constant E is an
energydensity obtained from the equation
10, 11
B
1
25
.-.
no
12, 14
C
D
E
1
7
7
90
50
50
...
...
800
no
no
yes
13, 15
16, 17
18
or•Ee-•/s27tq
2dq
=En
(19)
where L is the value of q at which the temperature due to
impact heating drops below somearbitrarily small value.
A significant fraction of Ex acts to heat material ejected
Numerical modelsof small impacts(Eg • 1016erg) per- during basin excavation. To estimate the amount of heat in
formed by O'Keefe and Ahrens[1976] suggestthat more than material thrown beyond the basin rim, we utilize a model for
90% of Eg goes into heating the projectile and target; let us nearsidecrustal structurederivedfrom gravity and topographcall this quantity En. While most of En goes toward heating ic data [Bratt et al., 1985a]. The difference between the asbasin ejecta,the resultsof O'Keefe and Ahrens[1976] indicate sumed pre-impact crustal thicknessand the thicknessof nonthat perhaps 25% of this heat is implanted in non-ejected mare crust beneath the youngestbasinssuch as Orientale protarget material and an additional unknown fraction of heated vides a lower bound on the depth from which material was
ejecta returns to rest within the basin. It is possiblethat less permanently excavatedfrom the basin. We remove from the
heat is ejected from the target region during a basin-size top of the target regiona plug of heatedmaterial of thickness
impact becauseexcavation of heated target material may have equal to the apparent depth of excavation (Figure 7). Left
been impeded by an abrupt increasein strength at the lunar behind is a thicknessof crust equivalent to that inferred at
Moho [Bratt et al., 1985a].
presentand a sphericalcap of heatedcrust and upper mantle.
The spatial distribution of anomalous temperatures pro- Though the return of heated ejecta probably contributed to
duced by shock heating under a large basin is largely un- the post-impact thermal structure of basins, we assume here
constrained.Though the distribution of impact-related energy that the contribution of returned ejecta to buried heat is small
density within the target region can be derived from cratering in comparison to that of shock heating of non-excavated
models [e.g., Gault and Heitowit, 1963; O'Keefe and Ahrens, target material. Let E• be the total quantity of impact heat left
1975], little consideration has been given to recovering the beneaththe final basin.Scalingargumentscited above suggest
temperature field from subsurfaceenergy density. For sim- that En may lie in the range 103• to 1035erg for Orientale.
plicity, we assumethat the implanted heat per unit volume The quantity En and the decay constant s are treated as free
decreasesexponentially with distance within a hemispherical parameters in the description of impact heating in the thermal
volume centered at the point of impact on the pre-impact models that follow.
surface[Kaula, 1979]. This geometryis illustratedin Figure 7.
An exponential decay of impact heat density is partially sup- Isotherm Uplift
ported by the geologicobservationthat shock metamorphism
Uplift of ambient crustal and mantle isotherms during
and melting are concentratedat shallow depths below terres- cavity collapse and basin formation may be treated as a
trial craters [e.g., Dence, 1971; Grieve and Cintala, 1981] and source of heat independentof impact heating. The extent of
by the roughly exponential relationship between the internal uplift heating may be estimated for young basins from the
energy density and depth in finite-differencemodels of the preservedrelief of the lunar Moho [Bratt et al., 1985a], the
formation of the Imbrium basin (Figure 5 of O'Keefe and basin age, and a temperature profile obtained from a global
Ahrens [1975]).
thermal history model. For simplicity, the uplift of isotherms
We compute the spatial distribution of impact-generated during basin formation is assumedto follow a vertical trajectemperatureas a function of slant-rangedistanceq- (r2 tory, with the maximum uplift occurringin the central region
+ z2)1/2from the centerof symmetryon the pre-impactsur- of the basin. The shape of the uplifted volume (Figure 7) is
face using the relation
assumedto be'that of a truncated cone with upper and lower
radii taken from the crustal structure modei of Bratt et al.
T(q)= 6e-q/s/pCv
(18)
[1985a]. The pre-impact temperature distribution is assumed
to be constant below 100 km depth. The anomaloustemperTABLE 2.
Adopted Values of Parameters Used in Thermal Stress
Models
Variable
Pc
Description
Value
Source
crustaldensity
2.9 g/cm3
Solomon[1975]
uppermantle
3.4g/cm3
Solomon
[ 1975]
1.2 x 107
erg/g øC
0.01 cm2/s
Solomonand
Longhi [1977]
Schatzand
Simmons[1972]
Baldridgeand
density
Cp
specificheat
k
thermal
diffusivity
volumetricthermal 2.7 x 10- 5 øC- •
expfinsion
E
Simmons
[1971];
coefficient
Skinner[1966]
Young'smodulus 7 x 10TMdyn/cm2 Mizutani and Osako
[1974]; Simmons
and Brace [1965]
ature distribution
is calculated
from the difference between the
uplifted temperature profile and the pre-impact temperature
profile.The temperaturechangecontributedby isothermuplift
is maximumat the surface
and at •he basincenterand,by
assumption,is zero at 100 km and greater depth.
TEMPERATURE AND THERMAL
STRESS
MODELS FOR ORIENTALE
Following the above guidelines,we presentmodels for the
contributions of isotherm uplift and impact heating to the
temperaturedistribution beneath the newly formed Orientale
basin. A summary of the models presentedbelow and the
associated
valuesof free parametersis given in Table 1.
Adopted valuesof physicalparameterscommon to all models
are given in Table 2.
12,424
BRATT ET AL.: THERMALSTRESS
NEAR COOLINGIMPACT BASINS
r, km
_20•00
200
I
0
I
200
I
I
60O
400
I
I
I
I
CRUST
I ORIENTALE
I
2O
E
6O
MANTLE
8O
IO0
Fig. 8. Structureof the crustand uppermantlebeneathOrientaledetermined
from an inversionof gravityand
topographicdata over the lunar nearside[Bratt et al., 1985a]. The dashedline at the baseof the crustdelineatesthe Moho
as computed
in the inversion
alonga profilefrom30øS,100øWto 5øS,85øW.The solidline represents
an azimuthally
averagedMoho profileusedin the estimateof isothermupliftin thispaper.
Isotherm Uplift
The shapeof the Moho beneathOrientale(Figure 8) providesa measureof the extentof uplift of lowercrustand upper
mantle during basinformation.This measureis strictlyonly a
lower bound, sincethe newly formed basin may have been
modified by such processesas long-term viscousrelaxation.
BecauseOrientale is the youngestlunar basin and preservesa
large amount of topographic relief, however, the effects of
long-term modification processesare thought to be minor.
The uplifted mantle (Figure 8) may be approximatedby a
truncatedcone with an upper radius of 50 km, a lower radius
of 310 km, and a heightof 55 km. From the estimatedage of
the basin (•-3.8 b.y.), the ambient temperatureprofile taken
from a global thermal history model [Solomonand Head,
1979], and the Moho relief shownin Figure 8, the anomalous
temperaturefield resultingsolelyfrom isothermuplift can be
estimated.Figure 9 showsthe pre-impactand post-uplifttem-
profile,but an estimatefor the error in the amount of uplift
beneathOrientale followsfrom the uncertaintyof about + 10
km in the crustalthicknessbeneaththe basin center[Bratt et
al., 1985a]. We have computed the basin thermal histories
subsequent
to isothermuplift by amounts10 km greaterand
lessthan for model A; temperaturesdiffer by lessthan 10%
from thoseshownin Figure 10.
The surfacedisplacements
and thermalstresses
predictedby
model A at several times after basin formation
T, øC
0
between these two curves. At the lunar surface AT
250
500
AT, øC
750
0/ • ' '• 'a
perature profiles beneath the center of Orientale as well as the
anomaloustemperaturedistribution, equal to the difference
AT
are shown in
Figure 11. The centerof the basinsubsides
(Figure 11a)about
20
0
250
500
' ' Ib
-
POST-
is
nearly 600øC.The initial anomaloustemperaturefield produced by isothermuplift is shown as a function of r and z in
Figure 10. The total anomalousheat contributedby isotherm
upliftbeneathOrientaleis 1.4 x 1032erg.
A thermal history model for the basin (modelA) in which
PRE-
_
.
60
-
70
-
80
-
90
-
uplift heating is the sole contribution to the anomaloustem-
peraturefieldis illustratedin Figure 10. By t = 10 m.y.(Figure
10b),much of the heat in the upper 20 km of modelA hasleft
the basinregion.By 100 m.y. (Figure 10c)only about 30% of
the initial heatremains.By 500 m.y.(Figure10d)lessthan 1%
of the heat is left. Thus most of the thermal contraction and
stresscontributedby isothermuplift will take placewithin 100
m.y. of basin formation for this model.
The major uncertainties in the contribution of isotherm
I00
Fig. 9. (a) Pre-impact
thermalprofile3.8 b.y.ago[Solomon
and
uplift to basinthermalevolutionare the adoptedpre-impact Head, 1979] and temperaturedistributionbeneaththe centerof the
newlyformedOrientalebasindueonlyto isotherm
uplift.(b)Anomatemperatureprofileand the extentand distributionof uplift.It
loustemperature
profilecontributed
by isotherm
upliftbeneath
the
is difficult,to assess
error in the adoptedglobaltemperature basin center.
BRATTETAL.' THERMALSTRESS
NEARCOOLINGIMPACTBASINS
12,425
I MODEL
AI
r, km
0
I00
200
300
_,ooo
200
b
t--O
I0 m.y.
3OO
O•
[
I
I
I
i
[
IOO
IOøC
200 _
c
300
100 m.y.
i
I
i
Fig. 10. Basinthermal evolution for model A. The initial field of anomaloustemperature(t = 0) is that producedonly by
isothermuplift. Also shownare the anomaloustemperaturefieldsat 10, 100, and 500 m.y. after basinformation.
0.2km in thefirst10m.y.andan additional0.2krnduringthe model A, the region of the basin where a, satisfiesthis crinext 90 m.y. The horizontal distribution of subsidenceis controlled by the horizontal extent of uplifted material beneath
the basin (Figure 8). By 500 m.y., a region out to 200 km
radius hasexperiencedat least 100 m of subsidence.
The amount of subsidencepredicted at the center of the
basin for model A (.--0.4 km) is about an order of magnitude
less than the observedrelief of the central basin depression.
Even if upper mantle isotherms were raised to the surface
during basin formation, the total accumulated subsidence
would not exceed 1 km. Thus, if a large portion of the relief
associatedwith the central depressionis a consequenceof
terion at 100 m.y. is from r = 230 to 400 km. Thus while the
magnitudesand signsof principal stressesfor this model are
consistentwith fissureformation, the predictedfissureswould
be at radial distancessignificantlygreater than observed.If
fissuresoriginated by thermal stress,we conclude that the
anomalousheat contributedby conversionof impact kinetic
energy must have been at least comparablein magnitude to
that contributed by isotherm uplift. Further, the effects of
impact heating were probably concentratedat lesserdistance
from the basincenterthan werethoseof isothermuplift.
thermal subsidence,an additional source of initial heat is re-
Impact Heating
quired.
The radial displacementu (Figure ,1l c) is toward the center
As discussedabove, the magnitude and distribution of
impact heatingare parameterizedby equations(18) and (19)
plus a correctionfor the quantity of impact heat carried away
from the excavatedcavity by heatedejecta.The crustal struc-
of the basin. The maximum value occurs between 150 and 200
,
km radial distanceand reaches200 m by 500 m.y. This value
is about half that of the subsidence of the basin center over the
same time interval.
ture beneath Orientale (Figure 8) suggeststhat at least 55 km
In the central basin regionboth horizontal stresses(Figures
l lb and 11d) are compressionaland similar in magnitude.
Becauseazz and all shear stressesare zero at the surface,
thrust faulting shouldbe the dominant mode of stressrelease
near the centerof the basin.Both stresscomponentsaccumulate most rapidly in the first 10 m.y. and reach 1.6 kbar by 100
m.y. With increasingradial distancer, aooapproacheszero. In
contrast,a, becomesextensionalat r greater than about 200
km (Figure l lb). The zone of maximum extensionala, is
locatedbetween250 and 350 km radial distance.By 100 m.y.,
a, reaches-0.4 kbar at r = 290 km.
As discussedabove, fissuringmost likely occurredwithin
100 to 200 m.y. after basin formation and in a stressregime
where a, was more negative than -0.2 to -0.4 kbar. In
vation of the central portion of the cavity. We have assumed
that the uppermost55 km of the hemisphericaldistribution of
impact heat (equation (18)) was transportedoutside the basin
as hot ejecta. The decay constants and the net quantity of
buried heat Ea remainingbeneaththe newly formed basin are
taken to be free parameters.Following our earlier discussion,
thickness
of shock-heated
crustwasremovedduringthe exca-
we beginby assumingthat Ea = 1032erg and we showlater
the effectof varyingthis poorly known quantity.
In Figures 12 and 13 are shown the initial distributions of
anomaloustemperatureand the coolinghistoriespredictedby
impactheatingmodelsfor Orientalewith Ea = 1032erg and
with s = 25 km (modelB) and 90 km (modelC). Most of the
initial heat in model B is concentrated within a small volume
near the basinsurface.The initial anomaloustemperatureim-
r, km
I00
I
200
I
I
,
$00
I -
: :
ß - - -
I '
400
-
m .•..__,
__•_.______
0.1
0.2
E
I••////
0.3
___
//
_
SUBSIDENCE
/
/ /500 m.y.
0.4
0.5
I
I
I
I
I
I
.-..... •.500 m.y.
1.5
•
I.O
RADIAL
\
_
STRESS
\
t=lOm.
\
0.5
i
i
I
r, km
0
I00
200
I
300
400
i
-O.O5
E
\\\
\
-0.20 -
IO•
•
////
/
500 m.y.
RADIAL DISPLACEMENT
-O. 25
2.0
- ----•
1.5
500 m y.
d
- IO••
•
•,•,•%
\
HOOP
STRESS
_
- I
Fig. 11. Displacementsand thermal stressesat the basin surfacefor model A (Figure 10). Curves shown represent
accumulatedvaluesat 10, 100, and 500 m.y. after basin formation.(a) Subsidencew; (b) radial stressa,,, (c) radial
displacementu, and (d) azimuthalor hoop stressaoo.
BRATTET AL.' THERMALSTRESS
NEAR COOLINGIMPACTBASINS
12,427
I MODEL
BI
r, km
I00
200
300
I
o
IOO
200
300
I
I
I
500 ø
••
?
i00o
/
I00ø /
IO0
200
I0 m.y.
i
I:: 3oo
•
i
o
IO0
50 o
3oc
IOøC
5o
2OO
_
I00 m.y.
500 m.y.
I
300
I
I,
I
I
Fig. 12. Basinthermalevolutionfor mod61B. The initial anomaloustemperature
field is due to implantedimpact
kineticenergy'the total heatEBburiedbeneaththe basinis 1032ergand the decayconstants is 25 km (seeequation(19)).
Also shownare the anomaloustemperaturefieldsat 10, 100,and 500 m.y. after basinformation.
mediatelybeneaththe centralbasinregionexceeds1000øC.By
100 m.y. after basinformation,only 27% of the initial energy
remains beneath the basin. The initial heat is distributed
the initial temperaturesare considerablyreduced. For the
•amereason,heatleavesthebasinmoreslowly.About60% of
over
the initial energy remains buried in the subsurfaceafter 100
m.y. The thermoelastic effects of cooling are illustrated for
a larger volume in model C relative to model B, and therefore
MODEL
r, km
I00
200
300
o
IOO
,
/i ø
i /
'i
/1 ' I /
i
200
300
,
,
'/
00
o
IOO
•
?50 / j
o
200
3OO
o
,':ø, .I
,
i
I
I
OiC
I0
:.y.
f=O
,.,
,
I
I
I
IO0
•
200
300
I
• i
5o
C
8ø
500 m.y.
,
I
I,
,
I, ,
I,
,,I
Fig. 13. Basinthermalevolutionfor modelC. The modelincludesimpactheatingwith Ea - 1032ergands -- 90 km. See
Figure 12 for further explanation.
12,428
BRATTET AL.' THERMALSTRESS
NEAR COOLINGIMPACTBASINS
r, km
0
I00
200
300
0.5 /'•-I00
m.y.
i.o
400
IMODEL
BI
500
m.y.
_
SUBSIDENCE
1.5
2.0 r
I
81 21.6{I
•
I
I
I
I
I
I
I
•
•
I
•
•
•
•
•
b_
_
61 •5.,• d•
4
-
RADIALSTRESS
t
!=I0m.y•
••••a•-•
••
•
-4 L
Fig. 14.
I
I
-
.........
•--•
,-
..........
500 m.y.
-
I
I
I
I
I
I
Surfacesubsidence
w and radial thermalstressa,, for basinthermalmodelB (Figure12). Curvesshown
represent
accumulated
valuesat 10,100,and500m.y.afterbasinformation.
and stress
modelsB and C in Figures14 and 15,respectively.
Shownin modelsindicatethe sensitivityof the displacement
eachfigureare w and a,, at the lunarsurfaceversusr and t. fields to the values of the parametersEa and s. The magand thermalstressscalelinearlywith
The shapes
of thecurvesfor u and aooandtheirrelationships nitudesof displacement
Ea, but the distributions
of thosequantitiesdependon s.
to w and a, are similarto thosefor modelA (Figure11).
Comparison
of Figures14and 15showsthat thepatternsof Therefore,if someportion of the reliefof the centraldepresaccumulated
displacement
andstressreflectthedistributionof sion and the band of fissuresare productsof thermal stress
the
initial heat (definedby s) in eachmodel.Most of the subsi- and if the elastichalf-spacemodeladequatelyrepresents
dencein model B is confinedto the first 100 m.y. and to radial
distanceslessthan 150 km. Subsidencenear r = 0 (Figure 14a)
response
of themoonduringthetimeof basinformationand
modification,
we may constrainthe quantityand distribution
of heatimplantedduringbasinformationby varyings soasto
is 1.8km by 100m.y.Subsidence
beneaththebasincenterfor
modelC (Figure14a)is lowerin magnitude
(only •0.2 km by match the horizontal extent of the central depressionand the
100m.y.)but takesplaceovera broaderregion.Also,because locusof fissuringand varyingEa so as to match a given
heatis lost moreslowlyin modelC, a significantproportionof
the total subsidencetakes place between 100 and 500 m.y.
Accumulated radial stress(Figures 14b and 15b) in the center
of both modelsis compressionaland exceeds1 kbar. Maximum extensional stressin model B occursbetween r = 90 and
130 km and accumulates to about -3 kbar. The distribution
fraction of the relief of the central depression.Of course,it is
importantto keepin mindthat the effectsof isothermuplift
(e.g.,modelA) will haveto be addedto the effectsof impact
heatingto estimatethe total thermoelastic
response
of the
moon to the basin formation event.
A modelfor impactheatingfollowingthe aboveguidelines,
of a, in modelC contains
a relativelybroaderregionof exten- model D, is shownin Figure 16a. For this model Ea = 7
X 1032ergands = 50 km. Significant
impactheatingextends
sion; maximumaccumulatedextensionalstressis -0.2 kbar
to
radial
distances
and
depths
comparable
to the radiusof
at 100 m.y.
temperatures
within150km
Neither model B nor model C satisfactorilypredicts the Orientale(310km).Near-surface
of basincenterexceedthe liquidustemperatures
of most iglocation of fissureswithin Orientale or matches the full magneous
rocks;
the
rate
of
cooling
in
this
model
is
underestinitude of relief of the central depression.However, these
__
BRATTETAL.'THERMAL
STRESS
NEARCOOLING
IMPACTBASINS
12,429
r, km
0
I00
200
300
400
ß.-'- '"" '""=
I•/
E
•o.:>
cI
/••
/
_
SUBSIDENCE
/500 m.y.
0.3
I
1.5
I
'"•
I
I
I
I
I
I
b
• ,X500
m.y.
-IO•',
1.0
I
•
X'N•\,
RADIAL
STRESS _
Fig. 15. Surface
subsidence
w andradialstress
a. forbasinthermalmodelC (Figure13).
mated for the first ,--10 m.y. becauseequation (2) does not
accountfor convectiveheat transport.By 100 m.y., 20% of the
The surface subsidence and radial stress for model D are
shownin Figure 17. The centerof the basin subsidesby 4.6
initial energyhas been lost; by 500 m.y. about 20% of Es
km after 500 m.y. This subsidenceis in addition to the 0.4 km
of subsidencecontributed by the loss of heat from isotherm
remainsin the target region.
I MODEL
DI
r, km
I00
' /I
IOO
2OO
200
/
300
I/
I
o
IOO
200
300
/
3000ø00//
/ -
•••.5o
ø50
oi I ••1it:øl
t/
3OO
o
I•1
10 ø (3
I
IOO
25 ø
_
250
ø
/
2OO
300
i••
1 ,
/
50 ø
Io
oc
500 m.y.
I
Fig. 16. Basinthermalevolutionfor modelD. The modelincludesimpactheatingwith EB- 7 x 10TMerg and s = 50
km. SeeFigure 12 for further explanation.
12,430
BRATT ET AL.' THERMAL STRESSNEAR COOLING IMPACT BASINS
r, km
0
I00
I
i
200
_ i-
-
:
-_ ;_
:300
-
4OO
-' -' i •
I
2 •.yd///
I
/
/
$UaS•OENCE
4r..//
5
I
I
I
I
I
I
I
34.2•
b
•
-
31.9
•',
-
19..5
. •\
-
•
_
RADIAL
STRESS
t = IOm.y.
.....-----
--
-2
I00m.y..•
.•
500m.y.
_
-4
Fig. 17. Surfacesubsidence
w and radial stressa, for modelD (Figure 16).
uplift (model A). The sum of the subsidence
from modelsA
and D accountsfor essentiallyall of the presentrelief from the
tensionala•r in Figure 17 is consistentwith the locationof the
band of fissures(150-230 km radial distance)within Orientale.
base of the central mare to the foot of the inner Rook Moun-
tains. Also, that most of the subsidenceoccurs at radial distances less than 200 km is in agreement with the observed
Effect of an Elastic BlockingTemperature
most extensional between about 100 and 250 km radial dis-
As discussedabove, material at sufficientlyelevatedtemperatures will not likely contribute significantlyto the thermal
stressfield. This effect has been parameterizedwith an elastic
blocking temperature[Turcotte, 1974, 1983] in thermal stress
model E depicted in Figure 18. In model E, the anomalous
temperature field contains contributions from both isotherm
uplift (model A) and impact heating. To determinewhether a
parcel of material is above or below the elasticblocking temperature Te,the ambient thermal gradient (Figure 9) must be
added to the anomalous temperature. We use a blocking temperature of 800øC, correspondingto the temperature at the
greatestdepth of earthquakesin terrestrial intraplate settings
[Chen and Molnar, 1983]. The use of a blocking temperature
tance. Between 10 and 100 m.y. after basin formation, the
does not affect the calculated subsidence,which should reflect
topographicprofile (Figure 2). Sincesomeof the relief of the
Orientale central depressionmay not be the result of thermal
contraction, the amounts of cooling and of subsidencein
model D shouldbe regardedas upper bounds.
By 100m.y.afterbasinformationin modelD, accumulated
valuesof a, reach nearly final values(Figure 17). This is in
agreementwith the inferredtiming of fissuringin the corrugated and plainsfaciesof Orientale.Near the centerof the basin,
a, and %o are compressional
and exceedthe compressive
strengtheven of unfracturedigneousrock at low confining
pressure,typically2-5 kbar [Brace, 1964]. Radial stressis
predictedlocationof maximumaccumulated
extensional
stress the combined solutions to the full thermal contraction probmoves from r = 140 to r = 180 km. The greatestextensional lem for the isotherm uplift and impact heating cases.
Model E (Figure18) combinesisothermuplift from model
stressreaches-2 kbar by 10 m.y. and -3 kbar by 100 m.y.
Thus evenby 10 m.y., a,, exceedsthe extensionalstrengthof
unfracturedrock at low confiningpressure[Brace, 1964]. Fis-
suringis likely within 10 m.y.of basinformationandwouldbe
A and impactheatingfrom modelD. Immediatelyfollowing
basinformation,temperatures
beneaththe centerof the basin
exceedTe at all depths.During early cooling,thermalstress
predicted to occur earlier if convectiveheat transport were
thus accumulatesonly in the shallow crust exterior to the
included in the thermal model. The location of maximum
regionsmostextensively
heatedby the basinformationpro-
ex-
BRATTET AL.' THERMALSTRESS
NEAR COOLINGIMPACTBASINS
12,431
r, km
:50
I00
i
I
••
I
200
I
I
$00
I
400
I
[MODEL
El
• • • ,500rn.y.
I00 m.y.
/.,• •
RADIAL
STRESS
t =10 rn.y.
I
I
I
I
Fig. 18. Surfaceradialstressa,, for modelE, a combination
of upliftheatingfrom modelA (Figure10)and impact
heating
frommodelD (œa= 7 x i032ergands = 50 km,Figure16).An elastic
blocking
temperature
Te of 800øChas
been assumed.
cess.This effect is reflectedin the shape of the a,, distribution
at 10 m.y. after basin formation. The zone of contraction contributing most to thermal stressduring this time interval
occurs not beneath the basin center but near r ~ 150 km,
where temperatures are below 800øC. The cooled, elastic surfacelayer is pulled toward this annular region,thus producing
zones of mild extension near r--0 and r- 300 km. By 100
m.y., most of the crust beneaththe basin has cooled below Te
and, as a result, has begun to contribute to and accumulate
thermal stress.By this time, the distribution of a, begins to
resemblemodels without a blocking temperature. The magnitude of a,, however, is everywhereless than in previous
models.This is especiallyevident near the basin center, where
a, in model D (Figure 17) exceeds30 kbar at 500 m.y. while
a, in model E is an order of magnitude less.The position of
the surface zone experiencing maximum radial extension is
strongly controlled by both the value of Te and the radial
extent of isotherm uplift beneath the basin. The result is a
region of extensional stress that is broader, smaller in the
magnitude of stress,and located at a greater radial distance
from the basin center compared to the same model without a
blocking temperature. In thermal stressmodels with lower
adopted valuesfor Te,theseeffectsare more pronounced.After
100 m.y. in model E, a, exceedsthe extensionalstrength of
igneous rock only for r > 250 km. Even though model D
provided a good fit to the topography and the location of
fissuring within Orientale among models not including the
effectsof a blocking temperature, model E demonstratesthat
with the inclusion of a blocking temperature a value of s less
than 50 km is necessaryto match the location of fissuringin
Orientale. If a blocking temperatureof 800øC is appropriate,
thermal
stress calculations
for models otherwise
similar
to E
indicate that s should be about 20 km to predict fissuring at
the distancerange observed.
[Church et al., 1982] and that the distribution of anomalous
temperaturesresultingfrom isothermuplift is relativelywell
known. Given theseassumptions,we note first that isotherm
uplift alone predictspoorly the locationof fissuringwithin
Orientale.It followsthat heat convertedfrom impactkinetic
energymust havebeenat leastas importantto the early thermal budgetof the basin.Expresseddifferently,EB is probably
comparableto or greaterthan 1032erg, the total amount of
anomalousheat contributedby isothermuplift.
The distribution of impact heating has been assumedin this
paper to follow an exponential decay with distance
characterizedby a fixed decay constant s (equation (18)).
When no blocking temperatureis considered,s must be about
50 km (model D, Figures 16-17) to predict correctlythe occurrenceof fissuringin the distancerange 150 to 230 km. With
the inclusionof a blockingtemperature(modelE, Figure 18),
an even greaterconcentrationof impact heat near the point of
impact is requiredto match the fissurepositions.We therefore
suggestthat the decay of impact heat density with distance
from the point of impact for an Orientale-size event must be
rapid and that for the exponentialparameterizationassumed
in this paper s must be less than or equal to 50 km. For
comparison,the energydensitydistributionshownin Figure 5
of O'Keefe and Ahrens [1975] for their numerical model of the
formationof the Imbrium basinfallsoff approximatelyexponentiallywith distancewith a decayconstantof about 20 km.
As a measure of the parameterization used here, with s = 50
km about half the buried impact heat lies inward of r - 100
km and 90% of the heat lies inward of r - 200 km.
If 5 km can be regardedas an upper bound on the thermal
subsidence
that has occurredwithin the centralregionof the
Orientalebasin,then the calculationsof this paperalsopermit
an estimateof an upper bound on EB. A superpositionof
model A (isothermuplift) and model D (Ea = 7 x 1032erg
and s = 50 km) accounts for the entire relief of the central
DISCUSSION
depression.
Further,if s is lessthan 50 km, as suggested
by the
The modelspresentedabovesuggestthat the emplacement thermal stressmodels that incorporatean elastic blocking
of heat during the formation of an impact basinand the subsequent loss of that heat were important contributors to the
topographyand tectonicsof lunar impactbasins.Beyondthis
qualitative result, we may use the results of these models to
place approximateconstraintson the quantity and distribution of impact heat implantedduring the formation of the
temperature, subsidenceat the center of the basin increasesfor
a givenvalueof E• (comparemodelsB and C, Figures14 and
15).On thesegrounds7 x 1032ergis an upperboundon Ea.
It should be recalledthat theseboundson Ea have been
estimatedwithout regard to sourcesof stressother than ther-
mal stress.The state of stressimmediatelyfollowing basin
Orientalebasin.Theseestimatesare basedon the assumption formation is unknown. Residualstressesmay have remained
that the observedfissuringis a product of thermal stress after shock release and cavity collapse, but such stresses
12,432
BRATTET AL.: THERMALSTRESS
NEAR COOLINGIMPACTBASINS
should have largely relaxed beneath the central basin region
because of the elevated temperatures. A persistent source of
stress that did not relax is that associated with basin topographic relief and its compensatio
n by lateral variation in density (e.g., crustal thickness)at depth. If the pre-mare basin was
in a state of nearly complete isostatic compensation, then the
basin relief would give rise to a horizontal stressof order pgh,
where p is the density, g is the gravitational acceleration, and
h is the variation in topography [e.g., deffreys, 1970, pp. 249268]. The Orientale basin inward of the Cordillera Mountains
lies below the level of surrounding terrain (Figure 2), which
would add a horizontal compressivestressat shallow depths
in the basin interior. The band of extensivefissuringoccursin
terrain 2 to 4 km below the local datum, suggestingthat 100200 bars of horizontal compressivestressshould be expected
from topography. This additional stress would have little
effect on the development of fissurespredicted by the stress
models except to delay slightly the time at which a, first
satisfied the criterion
The calculations
for extensional
of subsidence
failure.
ure.
On the basisof the thermal stressmodels,the topographic
relief of the central basin depressionand the range of radial
distancesfrom basincenterover which extensivefissuringoccurred constrainthe magnitudeE• and distributionof kinetic
energy that was convertedto buried heat beneath the newly
formed Orientale basin. E• must be comparableto or greater
than 1032erg because
the contributionof impactheatingto
and the inferred
constraints
on E• and s were obtained without considerationof the specific volume change that accompanies freezing. Several of the
basin thermal models have initial temperatures well in excess
of that necessaryto induce melting (Figures 12 and 16). The
temperaturesimmediately beneath the central basin region are
probably unrealisticallyhigh in thesemodels,a consequence
of neglecting the heat of fusion and of the simplistic exponential relation for the distribution of impact heat. Geological arguments and scaling from melt volumes in terrestrial
craters suggestthat the Orientale melt sheet has an average
thickness inward of the Outer Rook Mountains
anelasticeffects.Thesesolutionshave been comparedwith the
topographic relief [Head et al., 1981], the location of extensional fissures,and the timing of fissureformation [Church et
al., 1982] in the relativelywell-preservedOrientale basin.
For all basinmodelsconsidered,basin coolingand accumulation of thermal stressis most rapid within 100 m.y. after
basin formation, in agreementwith the inferred timing of ilssuring within Orientale. The predicted state of stressin the
region of fissuring (a, extensional,aoo compressionaland
smaller in magnitude) predicts well the form and orientation
of fissuresif thesefeaturesare the product of extensionalfail-
of about 1 km
[Head, 1974]. The additional subsidence
contributedby freezing of this melt sheetshould not exceeda few hundredmeters.
In the basin thermal models,of course,it is the integratedheat
rather than any given value of initial temperaturethat is important for the subsidenceproblem.
If we accept that Ea representsabout 25% [O'Keefe and
Ahrens, 1976] of the original kinetic energy E s of the impacting projectile and we use the bounds on E• suggestedabove,
thermal stressmust be at least comparableto that of isotherm
uplift. E• must be lessthan or equal to 7 x 1032erg in order
to be consistentwith the topographyof the central basin depression. The impact heat was concentrated within 100-200
km of the point of impact.
It is important to emphasizethat there is an untested ele-
ment of uncertaintyin the ability of our modelsto represent
the earliestportionsof basinthermalhistoryand the anelastic
responseof material at high temperatureto cooling. The
modelspresentedhere nonethelesssuggestthat cooling and
thermal stresscontributedsignificantlyto the topographyand
tectonics of multi-ringed basins and that constraints on the
quantity and distribution of impact heat emplaced during
basin formation may be derived from geologicalobservations
of the youngestbasinson the moon and on other planets and
satellites.
Acknowledgments. We thank W. F. Brace and C. H. Thurber for
helpful discussions,Jay Melosh and an anonymous reviewer and associate editor for constructive criticism of an earlier draft, and Jan
Nattier-Barbaro for assistancewith manuscript preparation. This re-
thenEs for the Orientaleeventwasin the range4 x 1032erg searchwas supportedby the NASA Planetary Geology and Geophysto 3 x 1033erg. Thesevaluesfor Es may be usefulfor esti- ics Program under grants NSG-7081 and NSG-7297.
mating scalingrelations of the form Es •- Dn for large impact
craters;scalingOrientale from Teapot-Ess,for instance,would
favor n _• 3.4-3.6, values similar to that derived by Valle
[1961] from small terrestrialcraters.The estimateof impact
kinetic energy derived here for Orientale may also provide
constraints on models of planetary accretion calling for the
impact of large planetesimalsand for modelsof the early thermal histories of planets in which the fractional conversionof
impact kinetic energy to heat and the spatial distribution of
that heat are important parameters[e.g., Kaula, 1979].
CONCLUSIONS
We have explored the hypothesisthat thermal stresshas
contributed significantlyto the topography and tectonicsof
lunar multi-ringed basins. Thermal models have been calculated for a variety of assumptionsabout initial basin heating
contributed by impact kinetic energy and uplift of isotherms
during cavity collapse and basin formation. Thermal stresses
and displacements have been calculated from the timedependent thermal models using analytic expressionsfor the
responseof an elastic halfspace. Some stressmodels have includedthe effectsof an elasticblocking temperature[Turcone,
1974, 1983] to account approximately for high-temperature
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12,433
(ReceivedJanuary 28, 1985;
revisedAugust 19, 1985;
acceptedSeptember9, 1985.)