Download Di}erential rotation of lithosphere and mantle and the driving forces

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PERGAMON
Geodynamics 17 "0888# 86Ð005
Di}erential rotation of lithosphere and mantle and the
driving forces of plate tectonics
Alan D[ Smitha\\ Charles Lewisb
a
b
Department of Earth Sciences\ National Cheng Kung University\ Tainan\ Taiwan\ R[O[C[
Department of Mining and Petroleum Engineering\ National Cheng Kung University\ Tainan\ Taiwan\ R[O[C[
Received 09 July 0885^ received in revised form 15 June 0886^ accepted 17 January 0887
Abstract
Uncertainties regarding the relative importance of basal drag and boundary forces in plate tectonic
models are a consequence of ~awed assumptions imposed by the use of the hotspot reference frame[
Velocities of lithospheric plates are in~uenced not only by lateral boundary forces\ but also by basal drag
forces resulting from Earth rotation[ Drag is exerted on the base of the asthenosphere and motion is
transmitted upwards to the lithosphere[ However\ as the transmission of stress in the mantle is viscosity!
dependent\ the reduction in viscosity through the asthenosphere results in plates su}ering a net westward
lag[ This {di}erential rotation| e}ect causes continental plates to be more strongly coupled to the deep
mantle as they are separated from the mesosphere by only relatively thin regions of asthenosphere[ For
such plates\ the calculated drag forces are of the same order of magnitude as the boundary forces[ Intraplate
volcanism during continental rifting and in opening basins is related to transverse convection cells set up
where topographic structures in the lithospheric root oppose mantle ~ow[ The motion of oceanic plates is
dominated by conventional plate boundary forces which may either reinforce or oppose drag from an
eastward mantle ~ow[ Reinforcement "e[g[\ Nazca plate# gives rise to Couette ~ow in the asthenosphere[
Opposition "e[g[\ Paci_c plate# results in counter~ow[ Shear stresses in both regimes are concentrated in
the upper asthenosphere and lead to melting of concentrations of hydrous minerals "{wetspots|# derived
from eroded continental mantle introduced by lateral asthenospheric ~ow[ Under a counter~ow regime\
melt collects in a stationary layer at shallow depth in the asthenosphere\ at the crossover point between
plate! and mesosphere!induced ~ow regimes[ Release of melt to the surface is governed by lithospheric
stress trajectories set up by convergence along plate boundaries[ Intraplate volcanism thus has a common
source although\ due to di}erent interactions between the boundary and drag forces\ asthenosphere ~ow
pro_les will di}er between basins\ giving relative motions between melting anomalies of a few centimetres
per year[ The overall e}ect\ however\ is to give an illusion of a series of quasi!_xed melting anomalies\
though in reality all these and the lithospheric plates are moving relative to the deep mantle[ Þ 0888
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A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
0[ Introduction
Soon after the acceptance of plate tectonics\ a revival of interest in Wegener|s contention
"Wegener\ 0804# that continental drift could be driven by tidal lag or rotational e}ects "Bostrom\
0860^ Nelson and Temple\ 0861^ Moore\ 0862^ Lliboutry\ 0863# was brought about by obser!
vations of westward drift of most plates at a rate of several centimetres per year relative to the
Antarctic plate "LePichon\ 0857^ Knopo} and Leeds\ 0861#[ As the Antarctic plate is centred on
the Earth|s south pole and is nearly surrounded by ocean ridges\ it can be regarded as an inertial
reference with regard to the Earth|s rotation axis such that the plate drift indicates a di}erential
rotation of the lithosphere and the mantle "Bostrom\ 0860^ Knopo} and Leeds\ 0861#[ Such
concepts were criticised by Jordan "0863# who\ while demonstrating tidal forces to be inadequate
for driving plate motions\ also refuted the entire concept of a net westward plate drift on the
grounds that it did not appear to agree with plate motions determined from the hotspot reference
frame[ The latter had been developed by Morgan "0860\ 0861# from Wilson|s hypothesis "Wilson\
0852# that the source regions of ocean islands were anomalously hot[ Morgan|s concept of
conduit!like upwellings appeared to o}er a readily useable absolute reference frame and was
adopted in many subsequent plate tectonic treatments[
Since the adoption of the hotspot reference frame\ however\ models have wrestled with the
need to combine drag and plate boundary forces as driving mechanisms for plate motions[
Boundary forces have been considered to predominate from observations that plate velocity
appears independent of plate area and plates attached to subducting slabs appear to be moving
the fastest "e[g[\ Forsyth and Uyeda\ 0864^ Chapple and Tullis\ 0866#[ Drag forces were envisaged
as a result of thermal convection cells acting directly on the base of plates\ but calculations
showed that to move plates at velocities of a few cm yr−0 by this mechanism would require mantle
~ow rates of 09 to 19 cm yr−0 "Bott\ 0873#[ Such velocities are di.cult to reconcile with the plume
model as the ascent velocity of plumes is estimated at about 09 cm yr−0 "e[g[\ Duncan and
Richards\ 0880#\ and mantle ~ow velocities close to or higher than this rate should result in
signi_cant motion between hotspots or the remixing of plumes with the convecting mantle
"Bott\ 0873^ Duncan and Richards\ 0880#[ The mantle convection velocities of around 0 to
4 cm yr−0 allowed in the plume model thus appeared consistent with the picture of plates
moving by boundary forces over a "near# static mesosphere\ with drag being considered to
be\ primarily\ a resistive force from observations "e[g[\ Forsyth and Uyeda\ 0864# that plates
with large continental masses "and hence thick lithospheric roots# appeared to be moving
slowest[
Plate boundary forces\ however\ cannot account for the tectonic record alone and\ at least for
large continental masses\ drag must also be an active force "Chapple and Tullis\ 0866^ Pavoni\
0881^ Ziegler\ 0881#[ Providing the mesosphere is not _xed\ continental drag could result from
entrainment of lithospheric roots within sub!asthenospheric convection cells "Stoddard and
Abbott\ 0885#[ The earlier concept of westward lithospheric drift also allows drag to result from
an eastward displacement of the mantle relative to the lithosphere as the Earth rotates[ It is
argued here that the latter di}erential rotation concept o}ers not only a solution to the debate
regarding driving forces\ but also a more complete explanation of the Earth\ where intraplate
volcanism becomes a part of\ instead of being superimposed on\ plate tectonics[
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
88
1[ Differential rotation] background
An internal explanation for a net westward drift of lithospheric plates lies with the thermal
and mechanical properties of the asthenosphere and its function as a zone of decoupling between
the rigid lithospheric plates and the deeper mesospheric mantle dominated by large!scale thermal
convection[ When the mantle is no longer _xed\ the mesosphere\ asthenosphere and lithosphere
can be envisaged as a series of shells of di}erent viscosities rotating about a central axis "Fig[ 0#[
A drag will then be exerted on the base of the asthenosphere by the movement of the mesosphere
as the Earth rotates[ The ~ow induced in the asthenosphere will in turn exert a drag on the base
of the lithosphere[ The mantle is thought to approximate a Newtonian ~uid "e[g[\ Bott\ 0873^
Middleton and Wilcock\ 0883#[ The transmission of stress through such materials depends on
viscosity\ with the result that a low viscosity asthenosphere will cause a lag of lithospheric plates
"Du^ Fig[ 0# relative to the deeper mantle\ which may alternatively be envisaged as eastward
mantle ~ow[
The asthenosphere is not homogeneous with regard to either viscosity or thickness due to the
presence of subducting slabs\ which may cool the region\ and continental mantle\ which may
lead to thermal insulation "Anderson\ 0871\ 0883#[ Lateral and radial variations in viscosity are
expected and should lead to di}erences in drag transmitted to individual plates[ The magnitude
of the plate lag\ Du\ will be greatest in the equatorial region and will decrease toward the poles
according to the cosine of latitude[ The e}ect is not likely to act purely eastÐwest as plate
movements continuously alter the mass distribution at the Earth|s surface[ The position of the
spin axis\ in turn\ responds to the mass distribution "Goldreich and Toomre\ 0858#[ A mass
anomaly which is not at the equator will be moved toward that position by tilting of the spin
axis\ also known as true polar wander "Anderson\ 0878#[ The in~uence of a given mass anomaly
will increase with an increase in distance from the centre of the planet[ The most stable con!
_guration relative to the kinetic energy of rotation is when positive mass anomalies lie in the
equatorial region[ Currently\ the largest lithospheric mass anomalies\ the subducted slabs in the
New Hebrides and northern Andes regions\ are distributed about the equator[ But in a dynamic
planet with di}erential rotation\ even a relatively stable con_guration will be short!lived[ The
rotation axis then moves in response\ with variations in its position imparting an undulating
pattern "Fig[ 0# with a wavelength of the order of 04999 km to the mantle ~ow pattern "Doglioni\
0889#[
2[ Relationship between rotation axis and hotspot reference frames
The westward plate lag of Du4 cm yr−0\ estimated by LePichon "0857#\ is an equatorial
average relative to the rotation axis[ In a more detailed treatment\ Knopo} and Leeds "0861#
found a net westward displacement of all plates except for Cocos and Nazca\ whose velocities
were poorly known because of the small sizes of these plates\ with by far the greatest lithospheric
angular momentum "VZPaci_c9[54VZEarth# belonging to the Paci_c plate[ With regard to the
directions and magnitudes of plate motions being di}erent to those in the hotspot frame\ it
should be noted that the fundamental assumption made by Jordan "0863# was that the plume
099
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
Fig[ 0[ The Earth as modelled as a series of shells rotating about a central axis[ Transmission of stresses through the
low viscosity asthenosphere in conjunction with the action of plate boundary forces causes a net westward lag of
lithospheric plates relative to the mesospheric mantle[ This lag constitutes a di}erential rotation of lithosphere and
mantle "Du# which can alternatively be seen as eastward mantle ~ow[ The magnitude of Du ranges up to 4 cm yr−0\
decreasing as cos f toward the poles[ Undulations in the mantle ~ow are caused as the position of the rotation axis
moves "polar wander# in response to plate movements changing the mass distribution at the Earth|s surface "after
Doglioni\ 0889#[
model is correct[ Plate!pair velocities used by DeMets et al[ "0889# in their NUVEL!0 model
where the Paci_c plate is _xed\ also agree well with those used by Knopo} and Leeds "0861# such
that we see no need to question the validity of the calculation made by these authors[
Rather\ it is the concept of hotspots _xed to deep mantle sources which should be questioned\
since if the mantle were _xed then no di}erential rotation should be observed in the hotspot
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
090
frame[ That requirements for di}erential rotation exist\ no matter which reference is used\ and
that the magnitude of the e}ect is smaller in the hotspot frame "9[7 to 2[5 cm yr−0^ Gordon and
Jurdy\ 0875^ Ricard et al[\ 0880# and varies depending on the chosen set of hotspots\ suggests
that the melting anomalies are shallow and moving[ The relationship of plate motions relative
to hotspots and to the rotation axis "Antarctic plate# as a reference was discussed by Lliboutry
"0863# whose vertical components of plate motion vectors "vZ# relative to the Antarctic plate\
are shown in Fig[ 1[ As illustrated in this _gure\ if the lithosphere and asthenosphere are 099 and
049 km thick\ respectively\ average lithospheric di}erential rotation rates of 0[6 cm yr−0 relative
to the hotspot frame "Ricard et al[\ 0880# and 4 cm yr−0 relative to a _xed Antarctic plate
"LePichon\ 0857# are compatible with hotspots representing melting anomalies at around 049 km
depth which move relative to both lithosphere and mesosphere[
Fig[ 1[ Vertical components of plate motion vectors relative to the Earth|s rotation axis in the hotspot frame "vZ
HRF# and for a _xed Antarctic plate "vZ RAR^ rotation axis reference# "after Lliboutry\ 0863#[ Average lithospheric
di}erential rotations of 0[6 cm yr−0 in the hotspot reference frame compared to 4 cm yr−0 relative to a _xed Antarctic
plate can be explained by the sources of intraplate volcanism lying at shallow depths in the asthenosphere[
091
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
3[ Magnitudes of forces
In conventional plate tectonic treatments\ movement of plates by boundary forces exerts a
drag on the top of the asthenosphere and induces a laminar "Couette# ~ow pro_le ðFig[ 2"a#Ł[
The velocity gradient and shear stress are invariant through the channel^ however\ as the ~ow is
induced by plate movement it is di.cult to conceive of how drag may be anything other than a
resisting and minor force[ In the di}erential rotation model\ drag is exerted on the base of the
mesosphere producing a ~ow where velocity decreases with height through the asthenosphere
Fig[ 2[ Possible asthenospheric ~ow regimes in conventional plate tectonic models using the hotspot reference frame
and in the di}erential rotation model where the rotation axis is used as a reference[ Flow equations are given in
Appendix 0[ For simplicity\ in this and subsequent diagrams\ the asthenosphere is depicted " following Montagner
and Tanimoto\ 0880^ Pavoni\ 0880# as a channel where decoupling takes place between the lithosphere and a
mesosphere characterised by large!scale thermal convection[ "a# Couette ~ow\ hotspot reference frame with _xed
mesosphere[ Movement of plates by boundary forces exerts a drag on the top of the asthenosphere[ "b# Couette ~ow\
di}erential rotation model[ Eastward movement of the mesosphere imparts a drag on the base of the asthenosphere
as the Earth rotates[ The ~ow induced in the asthenosphere causes a drag on the base of the lithosphere[ "c# Plate
boundary forces supplementing mesospheric drag as in the example of the Nazca plate[ When boundary forces
predominate\ the result is a Couette ~ow pro_le with diminished velocity gradient[ "d# Counter ~ow\ hotspot reference
frame with _xed mesosphere[ Movement of plates by boundary forces is balanced by asthenosheric ~ow in the opposite
direction "after Turcotte and Schubert\ 0871#[ "e# Counter!~ow\ di}erential rotation model[ Flow is induced by
opposing movement on both upper and lower boundaries of the asthenosphere[ The situation illustrated corresponds
to an oceanic plate moved westward by boundary forces[
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
092
ðFig[ 2"b#Ł[ Drag forces may be estimated from the velocity di}erential\ Du\ between lithosphere
and mesosphere "Bott\ 0873#[ In associated angular momenta calculations\ the dominant com!
ponent is vertical "pointing along the rotation axis# with the sign "negative# indicating a westward
lag of the lithosphere "Knopo} and Leeds\ 0861#[ Using generally accepted parameters for the
asthenosphere and lithosphere gives a shear stress at the base of the lithosphere of around
0[9 MPa for the scenario depicted in Fig[ 1[ More detailed models for individual plates are
presented in Table 0 for forces acting on the Africa\ Nazca and Paci_c plates\ as these demonstrate
the three potential con_gurations of dragÐboundary force interaction[ In our model\ the astheno!
sphere under continental plates varies in thickness from 14 to 49 km\ while for oceanic plates the
asthenosphere is assumed to lie between 099 and 199 or 149 km depth corresponding to the
estimates of Elsasser "0858# and Anderson "0878#[ Viscosities ranging from 0×0908 to 0×0919 Pa s
correspond to the values given by Davies and Richards "0881#[
In the case of continental plates such as Africa\ stresses will be modi_ed by the existence of
thicker lithospheric roots reducing the thickness of the asthenosphere "Fig[ 3#[ The limiting case
for a continental plate would be when the continental "lithospheric# mantle is su.ciently thick
to preclude the existence of any underlying asthenosphere[ Momentum would then be transferred
from the deep mantle directly to the lithosphere so that the continent would appear to be _xed
relative to the mantle[ With the exception of the Antarctic plate which is located on the pole
where Du is zero\ the continent which most closely approaches this scenario is Africa which has
been depicted as stationary or as showing only a small lag relative to the rotation axis reference
"Knopo} and Leeds\ 0861^ Lliboutry\ 0863#[ The drag forces of 1 to 09×0908 N estimated in
Table 0 for Africa " for Du −0 cm yr−0^ Knopo} and Leeds\ 0861# are in good agreement with
the estimates of Chapple and Tullis "0866# and are comparable to or exceed the combined e}ects
of slab pull and ridge push "total 2[1×0908 N# for this plate[
Primarily because of the in~uence of slab pull\ the boundary forces acting on oceanic plates
tend to be greater than those on continental plates[ Asthenospheric ~ow pro_les are thus expected
to be modi_ed by conventional plate!induced drag of the type envisaged in the hotspot model[
If boundary forces act in the same direction as eastward mantle ~ow\ as in the example of the
Nazca plate\ velocities in the asthenosphere will be enhanced ðFig[ 2"c#Ł[ Flow will then resemble
the Couette pro_le depicted for plate movement in the hotspot reference frame ðFig[ 2"a#Ł\ but
as shear stresses depend on the velocity di}erential\ drag will be reduced[ For the Nazca plate\
the shear stress acting on the base of the plate due to eastward mantle ~ow is calculated to be
9[0 to 9[3 MPa\ hence drag forces will be less than 4) of the combined e}ects of ridge push and
slab pull for this plate[ An additional drag force "FDR ?^ Fig[ 4# would also act on those parts of
the subducting plate in the asthenosphere although\ for the Nazca plate\ this is estimated to be
less than 09) of the drag force on the base of the plate under the ocean basin[
For plates with westward!dipping slabs such as the Paci_c plate\ motion in response to
boundary forces will induce asthenospheric ~ow in opposition to that arising from mesospheric
drag[ The resulting ~ow pro_le "Fig[ 2"e# and Fig[ 4# will resemble counter!~ow models in the
hotspot frame such as those described by Turcotte and Schubert "0871#\ although there are
signi_cant di}erences[ Counter!~ow in the hotspot frame ðFig[ 2"d#Ł is a combination of Couette
~ow induced by lithospheric drag and pressure!gradient ~ow[ The latter may represent either a
return ~ow of material to the ridge\ or asthenosphere displaced by a subducting slab[ Imposing
a _xed lower boundary causes steep velocity gradients and hence high shear stresses through the
093
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
Table 0
Magnitudes of boundary and drag forces for selected plates in the di}erential rotation model
Plate
Plate Area Ridge
"095 km1# length
"091 km#0
Africa
68
47
Nazca
04
43
Paci_c
097
008
Ridge push
"0908 N#1
Trench length
"091 km#0
Flow type
"Equation*
Appendix 0#
Plate
velocity u9
"cm yr−0#
0[7
Couette "b#
¦3[9
41
09[3
Couette "c#
¦7[4
002
11[5
counter!~ow "e#
−4[9
0[3
0[2
2[9
8
Slab pull
"0908 N#2
0
Ridge and trench lengths are e}ective lengths as calculated by Forsyth and Uyeda "0864#[
Assuming ridge push1[4×0901 N m−0 "Bott\ 0880#[
2
Assuming slab pull1[9×0902 N m−0 "Fowler\ 0889#[
3
Drag forces on the Africa and Paci_c plates were calculated assuming equatorial values for Du[ The calculation
for the Nazca plate assumes it is centred about latitude 19>S[
4
Negative values indicate drag acting in opposition to boundary forces[
1
~ow pro_le\ such that a plate velocity of 4 cm yr−0 ðFig[ 2"d#Ł results in shear stresses of 1[1 MPa
on the base of the lithosphere "Turcotte and Schubert\ 0871# which for a Paci_c!size plate would
equal slab!pull[ In contrast\ the parabolic part of the counter!~ow pro_le in the di}erential
rotation model is not symmetrical with the result that shear stresses are less than half as strong
as those in the hotspot frame counter!~ow model "note] in Fig[ 2"e#\ ~ow corresponds to
Du09 cm yr−0 while ~ow in Fig[ 2"d# only corresponds to Du4 cm yr−0#[
4[ Continental rifting
Continental rifting\ as for both the opening of the Atlantic in the Mesozoic and the break!up
of eastern Gondwana in the midÐlate Paleozoic\ is usually initiated at equatorial latitudes and
tends to follow pre!existing lineaments or sutures which cut the lithosphere "Sykes\ 0867^
Doglioni\ 0889^ Smith\ 0882#[ The sutures act as lines of weakness from the mechanical standpoint
and from the presence of low melting point hydrous minerals remaining from subduction activity
which brought the continental blocks together[ Preferential break!up of continents in the equa!
torial region may be attributed\ in part\ to ~exing and hence weakening of the plates as they
cross the Earth|s equatorial bulge "Turcotte and Oxburgh\ 0862#[ However\ sutures orientated
northÐsouth and\ hence\ opposing the eastward asthenospheric ~ow " _rst order rifts^ Doglioni\
094
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
Di}erential
rotation Du3
"cm yr−0#
−0[9
Asthenosphere
viscosity "m#
"Pa s#
3×0908
0×0919
¦2[4
0×0908
3×0908
−09
0×0908
3×0908
Lithosphere
thickness "hL#
"km#
064
049
064
049
099
099
099
099
099
099
099
099
Asthenosphere
thickness "h#
"km#
14
49
14
49
099
049
099
049
099
049
099
049
Shear stress
"tL# "MPa#
9[49
9[14
0[14
9[52
9[09
9[96
9[39
9[17
−0[29
−9[69
−4[29
−1[57
4
Drag force4
"0908 N#
2[84
0[87
8[77
3[87
9[04
9[00
9[51
9[31
−03[9
−6[45
−46[1
−18[1
Example
" _gure#
2b
2c
2e
0889#\ tend to be reactivated preferentially\ suggesting important controls on the rifting process
by di}erential rotation e}ects which will also be at their greatest at low latitudes[
Drag forces acting on the lithosphere will depend on the thickness of continental mantle keels
and particularly for large continental con_gurations\ may act in di}erent directions depending
on the position of the continent above the undulations in the mantle ~ow pattern[ Topographic
variation at the continental mantleÐasthenosphere interface may also induce small!scale con!
vection cells in the asthenosphere "Smith\ 0882^ King and Anderson\ 0884#[ Following the
opening of an ocean basin\ convection would be expected to take the form of transverse rolls of
the type described by Richter "0862#[ Correlations between lithospheric structure and intraplate
volcanic tracks have long been documented "LePichon\ 0857^ Marsh\ 0862^ Mitchell\ 0875#[
Further inspection reveals that ~ood basalts tend to be located above the intersection of major
sutures in the continental lithosphere\ while intraplate volcanic tracks in the ocean basin extrapo!
late into sutures:lineaments which intersect the axis of rifting at some angle[ The correlations
suggest intraplate volcanism results from melting of eroded continental mantle as it is cycled
toward the ridge axis "Smith\ 0882#[ As the basin opens\ the convection cells expand\ giving the
impression of stationary volcanic sources[ The model is somewhat similar to that of King and
Anderson "0884# for ~ood basalt generation around the margins of cratonic blocks\ but provides
an explanation for the three dimensional extent of the basalt provinces and the position of
volcanic tracks extending from these provinces[
095
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
Fig[ 3[ Schematic illustration of forces acting on continental plates as illustrated by opening of the South Atlantic[ "a#
A thinner keel under South America would result in a reduction in drag force "FCD# on the eastern part of the plate
thereby contributing to continental break!up in conjunction with trench suction "FSU# along the eastern margin of the
Paci_c basin[ Rifting followed a pre!existing _rst!order suture "dashed line YÐZ^ suture of Pan!African Adamastor
basin# which acts as a line of weakness[ "b# Ridge push "FRP# may become important after opening of the basin[
Intraplate volcanism is found where second!order sutures "dashed line WÐX^ Damara belt# intersect the axis of rifting
suggesting an origin related to erosion and cycling of geochemically!enriched continental mantle toward the ridge axis
"MAR] Mid Atlantic Ridge# by local asthenospheric convection taking the form of transverse rolls[
The rifting of South America from Africa is used as an illustration of the above points in Fig[
3[ Opening of the South Atlantic followed the pre!existing suture of the Pan!African Adamastor
Ocean[ A thinner lithospheric keel under South America would have resulted in drag forces being
reduced under the western part of the continental mass prior to rifting[ The Cameroon LineÐ
Benue Trough and Walvis RidgeÐDamara belt provide examples of intraplate lines extrapolating
into lithospheric sutures\ while the Parana ~ood basalt province overlies thin lithosphere where
the sutures of the Adamastor and Damara basins intersect "Smith\ 0882#[ The East African rift
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
096
Fig[ 4[ Forces acting on oceanic plates in the di}erential rotation model as illustrated by a NWÐSE transect across
the modern Paci_c basin parallel to direction of asthenospheric ~ow[ Of the forces identi_ed by Forsyth and Uyeda
"0864#\ slab pull "FSP#\ slab resistance "FSR#\ collisional resistance "FCR#\ trench suction "FSU# and transform resistance
"FTR# act as in plate tectonic models which use the hotspot reference frame[ In the eastern part of the basin\ ~ow
pro_les induced by mesospheric drag and boundary forces act in the same direction\ giving rise to Couette ~ow under
the Nazca plate[ In contrast\ con~icting patterns of ~ow induced by mesospheric drag and plate boundary forces set
up a counter~ow regime under the Paci_c plate[ Melts produced from shearing of eroded continental mantle in
enriched asthenospheric domains\ collect in a stationary layer ðu9^ see Fig[ 2"e#Ł at shallow level in the asthenospheric
~ow pro_le[ Release of melt from this layer is governed by stress trajectories in the overriding plate "see Fig[ 6#\ giving
rise to ocean island volcanism[ The pattern of upwelling under the East Paci_c Rise "EPR# as observed in tomographic
pro_les "e[g[\ Anderson\ 0878#\ corresponds to the sum of asthenospheric ~ow patterns under the Paci_c and Nazca
plates[ Westward dipping slabs owe their steep angles to their opposition to mantle ~ow "the {nail e}ect| of Doglioni\
0889# and thereby may su}er an additional resistive force\ FSR ?[ Conversely\ the shallow angles of eastward!dipping
slabs may result in an additional drag force "FDR ?# as the part of the slab in the asthenosphere will also be subject to
drag forces[
is also orientated perpendicular to the mantle ~ow^ however\ the rift system cuts Precambrian
basement where there is no well!de_ned line of crustal weakness\ and lies both north and east of
thick lithosphere "×114 km^ Fairhead and Reeves\ 0866^ Pollack and Chapman\ 0866# under the
major cratonic blocks of the continent[ Drag forces would be expected to be lower on the eastern
side of Africa which would not be conducive to progression of the rift system[
5[ Mantle domains
Hydrous minerals in the continental mantle would likely carry EM " following the terminology
of Zindler and Hart\ 0875# isotopic signatures[ Sutures would also be sites for veining of the
continental mantle by small melt fractions from the asthenosphere "McKenzie\ 0878^ Smith\
0882\ 0887#[ Although asthenosphere!derived melts would inherit the DM isotopic composition
of their source\ the partitioning of parent:daughter elements would result in such melts evolving
to HIMU isotopic compositions on solidi_cation in the continental mantle[ Hence local regions
of the continental mantle may exhibit the range of isotopic signatures found in intraplate
097
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
volcanism[ Continental mantle eroded into the asthenosphere and not immediately tapped on
rifting\ or delaminated during continental collision events\ would produce shallow domains
containing geochemically enriched material comparable to the {perisphere| of Anderson "0885a#[
Di}erential rotation will result in such domains moving to the east of the continent under which
they form\ thus providing a means for the lateral introduction of source material for intraplate
volcanism into the oceanic asthenosphere[
Large!scale delamination of the continental mantle has been suggested as the reason for the
distinct isotopic signature of Indian Ocean MORB "Mahoney et al[\ 0878#\ and the di}erential
rotation e}ect provides an explanation for why Indian Ocean!type asthenosphere should cur!
rently be moving under the western Paci_c as proposed by Crawford et al[ "0884# and Hickey!
Vargas et al[ "0884#[ The Indian Ocean domain can be seen as replacing older asthenospheric
domains whose history can be traced to PaleozoicÐMesozoic events along the western margin of
the paleoÐPaci_c basin ðFig[ 5"aÐc#Ł[ Rifting events along the eastern margin of Gondwana
during the midÐlate Paleozoic detached continental fragments such as North China\ South China\
and Indochina which then migrated north to form Asia "e[g[\ McElhinny et al[\ 0870#[ Thinning
of the lithosphere of at least one of these blocks "North China^ Menzies et al[\ 0882# may have
taken place during rifting from Gondwana in the mid!Paleozoic "Smith\ 0887#[ At a di}erential
rotation rate of 3 cm yr−0 "appropriate for mantle at latitude 29>S^ Fig[ 0# a domain formed
under eastern Gondwana in the mid!Paleozoic would now lie 03999 km to the east\ underlying
most of the South Paci_c[ Mantle domains in the South Atlantic\ Indian Ocean\ and South
Paci_c may thus all share a common origin related to erosion of Gondwanan thermal boundary
layer material[ The extent of these domains corresponds to the near globe!encircling DUPAL
anomaly of Hart "0873# ðFig[ 5"d#Ł[ A corresponding North Paci_c domain\ containing mech!
anical boundary layer material delaminated when blocks collided to form Asia in the PermoÐ
Triassic\ would now underlie Hawaii in the northern mid!Paci_c[
000000000000000000000000000000000000000000000000000
4
Fig[ 5[ Westward lag of the lithosphere through the Phanerozoic relative to the positions of mantle domains produced
by erosion:delamination of continental mantle into the asthenosphere during continental rifting:collision events[ Plate
reconstructions are based on the maps of Scotese et al[ "0868# and Coney "0889# and terrane accretion models of
Debiche et al[ "0876# and Stone and McWilliams "0878#[ Abbreviations\ continents and terranes] AF] Africa\ AN]
Antarctica\ AU] Australia\ EU] Eurasia\ IC] Indochina\ IN] India\ NA] North America\ NC] North China\ SA] South
America\ SC] South China\ IT] Insular terrane^ oceanic plates] FA] Farallon\ IZ] Izanagi\ PA] Paci_c\ PX] Phoenix[ The
model demonstrates the suitability of di}erential rotation as a mechanism for the lateral introduction of geochemically
enriched material into the oceanic asthenosphere to serve as the source of intraplate volcanism[ Migration of the
domains corresponds to an average rate of 3 cm yr−0[ No attempt has been made to take into account dispersion of
domains by localised convection such as would be associated with ridge systems[ "a# DevonianÐCarboniferous[ Erosion
of thermal boundary layer continental mantle during the fragmentation of eastern Gondwana creates a South Paci_c
domain[ "b# PermianÐTriassic[ Mechanical boundary layer continental mantle delaminated during the collisions of
the Siberian\ North China\ and South China continental blocks gives rise to a North Paci_c domain which currently
underlies Hawaii[ "c# Mid Cretaceous[ Further contamination of the asthenosphere with Gondwanan continental
mantle occurs on opening of the South Atlantic and Indian Oceans "see also Fig[ 3#[ The North Atlantic is bordered
by younger lithosphere and the geochemical composition of this domain is distinct[ "d# Present[ Di}erential rotation
explains the appearance of Indian Ocean asthenosphere in the western Paci_c[ The domains contaminated with
Gondwanan continental mantle comprise the DUPAL anomaly of Hart "0873#[
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
098
009
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
6[ Intraplate volcanism in long!lived basins
In the Paci_c basin\ Eocene to Recent intraplate volcanism is concentrated into three zones
spaced 0499 to 1999 km apart "Fig[ 6#[ In the west\ these zones coincide with major changes in
orientation along the margin of the Paci_c plate\ while in the east the zones correlate with plate
boundaries within the ocean basin or major fracture zones along the East Paci_c Rise "Lewis
and Smith\ 0884#[ From south to north\ the Louisville\ CookÐAustralÐMarquesas\ and Hawaiian
Fig[ 6[ EoceneÐRecent intraplate volcanism in the Paci_c basin appears to follow major zones "shaded# representing
stress trajectories where the average maximum horizontal shear stress "sH# has been enhanced by plate interactions
along the margins of the basin[ Most volcanism occurs where the zones intersect eastward!migrating domains of
asthenosphere contaminated with eroded:delaminated continental mantle "see also Fig[ 4 and Fig[ 5#[ Solid arrows
indicate plate motions relative to a _xed Antarctic plate[ Abbreviations\ plates] PA] Paci_c\ CO] Cocos\ NZ] Nazca\
PH] Philippine^ ocean islands and plateaus] A] AustralÐCook\ C] Caroline\ CE] CobbÐEickelberg\ F] Foundation\ H]
Hawaii\ KB] KodiakÐBowie\ L] Louisville\ MQ] Marquesas\ PG] PitcairnÐGambier\ S] Society\ SA] Samoa\ SG] Sala
y Gomez[ Mercator projection[ Numbers indicate age ranges in million years[
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
000
chains are parallel to the EltaninÐHeezen fracture zone system\ the NazcaÐPaci_c plate boundary\
and the Quebrada fracture zone\ respectively "Fig[ 6#[ A further zone of ocean islands is possibly
represented by the KodiakÐBowie and CobbÐEichelberg chains\ although the MORB!like iso!
topic signature of these "Hegner and Tatsumoto\ 0878# suggests they are more likely to represent
seamounts related to axial ridge processes rather than true examples of intraplate activity[
The distribution of Paci_c intraplate volcanism is therefore far from random as portrayed in
most hotspot models\ but is consistent with earlier concepts of convective rolls or stress _elds
"e[g[\ Shaw\ 0858\ 0862^ Richter\ 0862^ Jackson and Shaw\ 0864#[ As pointed out by Richter
"0862#\ upwelling associated with transverse rolls would not be stable with fast plate velocities
and would be transformed into longitudinal rolls with axes perpendicular to the ridge system[
The spacing of the zones of Paci_c intraplate volcanism is consistent with an aspect ratio of 2]0
or 3]0 for upper mantleÐsize convection cells[ Some support for the existence of convective rolls
has recently come from tomographic data "Katzman et al[\ 0886#[ However\ di}erences in width
between the zones identi_ed in Fig[ 6 "the CookÐAustral zone would be as wide as the convective
rolls# are di.cult to reconcile with secondary convection being the primary cause of volcanism[
The required aspect ratio is also greater than that suggested by Richter "0862#\ and even more
so if the convection cells were to be con_ned to the asthenosphere[
Alternatively\ Shaw "0862# proposed that intraplate volcanism\ using Hawaii as an example\
could be explained by the intersection of horizontal and vertical stress trajectories\ with the
apparent episodicity of eruptions re~ecting thermal buoyancy and accumulation of melts in
shallow source regions[ Changes in orientation along plate boundaries are a source of stress\
which due to the rigidity of plates\ could be transmitted across the Paci_c lithosphere[ The zones
of intraplate volcanism in Fig[ 6 may thus mark lithospheric stress trajectories "enhanced SH and
SV following the terminology of Zobak\ 0881# set up by the lag of the Paci_c plate relative to the
mesosphere being greater than that of the Eurasian or Indian plates[ The horizontal stress
trajectory postulated by Shaw "0862# can be equated with shearing in the asthenosphere[ Turcotte
and Schubert "0871# calculated that shearing of asthenosphere with viscosity of 3×0908 Pa s
would result in temperature increases of only a few degrees[ Such heating would not be adequate
to cause melting on the anhydrous peridotite solidus which lies some 199 degrees above the typical
normal asthenosphere adiabat "potential mantle temperature of around 0179>C#[ However\ many
petrological models "Tuthill\ 0858^ Flower et al[\ 0864^ Bonatti\ 0889^ Francis\ 0884^ Francis and
Ludden\ 0884# have argued for volatile!rich sources for intraplate volcanism[ The solidus for
hydrous peridotite lies very close to the normal asthenosphere adiabat^ indeed hydrous minerals
may only be stable in the cooler regions of the asthenosphere away from ocean ridges[ The
temperature increases from shearing\ supported by the thermal feedback mechanism of Shaw
"0858# for regions under continuously applied stress\ would then be a feasible cause of melt
generation[ Eroded continental mantle would also be potentially cooler and more viscous than
the surrounding asthenosphere\ allowing enhanced survival of hydrous minerals but a greater
temperature increase on shearing[
The asthenospheric ~ow pro_le in Fig[ 2"e# predicts the existence of a stationary layer charac!
terised by high shear stress at the crossover point between opposing ~ow regimes[ In the isoviscous
section in Fig[ 2\ this crossover layer is in_nitely thin\ but under real conditions where viscosity
may vary both laterally and horizontally\ it would be expected to take the form of patches where
melts generated by shearing of domains containing low!melting point minerals would collect[
001
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
The layer would therefore function as the pockets of melt postulated by Shaw "0862#[ Phlogopite\
but not amphibole\ would be stable at depths greater than 099 km[ The stationary melt accumu!
lation layer would rise to shallower depth with decreasing mesospheric velocity "higher latitude#\
higher plate velocity\ or decreasing asthenospheric thickness\ such that\ under oceanic plates less
than 099 km thick\ it could potentially lie within the stability _eld of amphibole[ If melt were
tapped when lithospheric stress trajectories "note] the asthenosphere immediately under the
lithosphere in Fig[ 2"e# behaves as the lithosphere# intersected this layer\ the result would be
analogous to the presence of a series of _xed\ deep!seated melting anomalies under the plate[
Cessation of volcanism in the absence of changes in the stress _eld can be explained by exhaustion
of low!melting point minerals[ Correspondingly\ intersection of a melt pocket by a pre!existing
lithospheric stress trajectory would cause release of melt\ giving the false impression that the
lithosphere had just been hit by the arrival of plume material[
Intraplate volcanism on the Nazca plate may be related to stress trajectories between transform
faults along the East Paci_c Rise and breaks in the subducting slab along the margin of South
America "Anderson\ 0885b#[ The main example of intraplate volcanism on this plate\ the Sala y
Gomez line\ does not show a linear age progression and was originally described as a {hotline|
by Bonatti and Harrison "0865#[ The volcanism can be explained by the ~ow regime under the
Nazca plate lacking a stationary melt collection layer so that melting anomalies would not appear
to be _xed points[
7[ Conclusions
Returning to the use of a _xed Antarctic plate as a reference for plate motions allows drag
forces to arise from Earth rotation imparting shear on the base of the asthenosphere from which
stresses are transmitted to the lithosphere depending\ to varying degrees\ on the thickness and
viscosity of the asthenosphere[ Interplay between drag and plate boundary forces results in the
asthenosphere being subject to pervasive shearing and partial melting as it functions as a zone
of decoupling between lithosphere and mesosphere[ Mantle ~ow rates involved in this model can
exceed 4 cm yr−0\ particularly for asthenospheric counter~ow regimes at equatorial latitudes and
are\ thus\ incompatible with the concept of mantle plumes[ The di}erential rotation mechanism\
however\ sets up its own internal explanation for the origin of intraplate volcanism which builds
on the concepts of stress _elds\ convective rolls and shear melting that were advanced in the
0869|s before adoption of the hotspot:plume model[ However\ unlike these earlier models\ an
intrinsic part of the di}erential rotation mechanism is the lateral introduction of geochemically
distinct material as {wetspots| to serve as sources for intraplate volcanism in long!lived ocean
basins[ Like ocean ridge and arc volcanism\ intraplate volcanism becomes part of plate tectonics
rather than being superimposed on it\ with a common source material "continental mantle# and
common mechanism of origin "large!scale plate interactions#[ As the asthenospheric ~ow pro_les
related to intraplate volcanism di}er between basins\ en masse motion between melting anomalies
is also an inherent feature of the model\ hence the di}erential motion between {hotspots| noted
by Molnar and Stock "0876# and references therein[ The concept of quasi!_xed melting anomalies
is still useful as a reference\ but not as an absolute frame since the melting anomalies are moving
not only relative to each other\ but also relative to the lithosphere and mesosphere[
A[D[ Smith\ C[ Lewis : Geodynamics 17 "0888# 86Ð005
002
Appendix A[ Calculation of asthenospheric ~ow pro_les and shear stresses
Variables]
u9lithospheric velocity
uasthenospheric velocity
u0mesospheric velocity
hthickness of asthenosphere between depths y9 and y0
hLlithospheric thickness
mdynamic viscosity
tshear stress
Equations] "a# to "e# correspond to the ~ow pro_les in Fig[ 2]
"a# Couette Flow "Turcotte and Schubert\ 0871#]
u"0:1m#"y1−hy#dp:dx for u99
In general\ u"0:1m#dp:dx"y1−hy#−u9y:h¦u9
tmdu:dy0:1"dp:dx#"1y−h#−mu9:h
if dp:dx9\ uu9 "0−y:h#\ tmu9:h
"b\c# Pressure drag ~ow "African and Nazca plates# "Bohme\ 0876#]
uu0¦"u9−u0#y:h−0:1m"dp:dx#"yh−y1#
if dp:dx9\ uu0¦"u9−u0#y:h and tm"u9−u0#:h "i[e[\ simple Couette ~ow#
"d# Counter!~ow\ hotspot reference frame with _xed mesosphere "Turcotte and Schubert\
0871#]
uu9"0−"y:h#¦5ð"hL:h#¦0:1Łð"y1:h1#−y:hŁ#
tu9mð"−0:h#¦5"hL:h¦0:1#"1y:h1−0:h#Ł
"e# Counter!~ow\ di}erential rotation model "Paci_c plate#]
u"5:h1#ð"u9hL:h#¦"u0¦u9#:1Ł"y1−hy#¦"u0−u9#y:h¦u9
tm:h"5:hð"u9hL:h#¦"u0¦u9#:1Ł"1y−h#¦"u0−u9##
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