Introduction
The stresses building up in the rigid outermost layer of the Earth are the
result of both shallow and deep geological processes. The dynamics of the
lithosphere is determined by a combination of plastic, elastic and viscous
flow properties of the lithospheric material ,
while the evolution of the sub-lithospheric mantle is predominantly driven by
viscous flow . It has been shown
that shallow processes influence both the magnitude and orientation of the
lithospheric stresses. Among such processes the most important are slab pull,
ridge push, trench friction and continental collision (deformation)
as well as cratonic root resistance .
Gravitational effects due to lateral density heterogeneities in the
lithosphere and tractions from the mantle flow at the base of the moving
plates also play an important role. Superposition of different tectonic forces
creates dissimilar orientations and regimes of the lithospheric stress field
in different regions, as shown by the World Stress Map project
.
Furthermore, on a global scale the intra-plate stress orientation follows a
specific pattern at a longer wavelength due to a large force contribution
from the convecting mantle . This
first-order stress pattern (long wavelength) is dynamically supported, as the
controlling forces correlate well with the forces driving the plate motion in
most continental areas such as North and South Americas and Europe
. and
used different approaches to show that the contribution
of the crust (shallow density structures) to the overall lithospheric stress
pattern is rather small compared to that of the mantle buoyancy forces,
amounting to ∼ 10 %, except for regions characterized by high
altitudes, especially the Tibetan Plateau, where the contribution is larger.
In these previous modeling studies, the effect of the crust was determined
separately by computing the gravitational potential energy from a crust
model, which was subsequently applied as a correction
. The contribution of the crust with a
shallow lithospheric density contrast generates the second-order pattern
(mid-to-short wavelength) in the stress field, mostly coming from topography
and crustal isostasy .
Likewise, the long-wavelength signal of the topography is related to the
vertical component of the stress field tensor originating from the thermal
convection of the mantle rocks . This
generates a high dynamic topography in regions of upwelling over the African
and Pacific large low shear velocity provinces (LLSVP) and low topography
above downwelling in the regions of subduction . In contrast, at a mid-to-short wavelength, topographic features are influenced by processes such as plume–lithosphere interaction
and small-scale
convection in the upper mantle .
However, the largest fraction of topography is caused by isostasy due to
variations in crustal thickness and density, as well as density variations in
the subcrustal lithosphere. Comparatively, the fit typically obtained between
the modeled dynamic and observation-based residual topographies is lower
, than
for the other mantle-flow related observables. For example, the modeled and
the observed geoid models give a relatively higher correlation due to the large contribution of the lower mantle but the
modeled geoid is sensitive to the choice of mantle viscosity
. One of the reasons for the poor correlation between
modeled and residual topographies is our insufficient knowledge of the
petrological properties of the upper mantle , for example
in relation to the chemical depletion of cratons in continental regions.
Hence, in this study, in addition to evaluating the influence of
thermal-density heterogeneities on lithosphere stress field and topography,
we test the impact of corrections for the continental depletion on the
topography and stress field.
Also, constraining the modeled lithospheric stress with observations is
challenging due to previously poor spatial coverage by World Stress Map
data . An alternative method
documented in the literature is to compare the strain rate estimated from the
modeled deviatoric stresses with the Global Strain Rate Map
. However, the lithospheric stress in plate interiors (i.e.,
far from the plate boundaries) is not well constrained with the Global Strain
Rate Map. Hence, a gradually increasing coverage of the observed global
stress field data serves as a motivation for studies attempting a global
comparison of the observed and modeled stress field patterns, including our
present study.
To date, two distinct approaches have been adopted to study the origin of the
lithospheric stress, and each has given a relatively good fit to the observed
stress field. On the one hand, have estimated the lithospheric
stress from a model that disregards the mantle flow contribution and used the
fit between modeled and observed plate velocities as a sole criterion. On the
other hand, , , ,
and have aimed at assessing the
influence of mantle flow on the lithospheric stress field and have shown that
the bulk mantle flow explains a large part (about 80–90 %) of the stress
field accumulated in the lithosphere , in both magnitude
and the most compressive horizontal direction. The aim of the present study
is to evaluate the contribution of the upper mantle density and viscosity
heterogeneities above the transition zone to the observed spatial stress
regimes of the lithosphere , while testing different
approaches and data sets used to describe the thermal and rheological
structure of the upper mantle and the crust. We use a 3-D global
lithosphere–asthenosphere finite element model with
visco-elasto-plastic rheology coupled to a spectral model of mantle flow
at 300 km depth. Deriving all force contributions from a
single calculation resolves any inconsistency that might arise from treating
individual force contributions to the stress field separately, as has been
done in earlier studies . As part of this work, we further
estimate dynamic topography and correlate our results with two different
residual topography models. One is based on seismic surveys of the ocean
floor used to correct for shallow contributions to topography and free-air
gravity anomalies on continents . The second model is taken
from and is based on actual topography corrected for
crustal thickness and density from CRUST1.0 . Both models are
also corrected for subsidence of seafloor with age.
Adopted from . (a) Depth-dependent scaling
profile of S-wave velocity to density; (b) radial mantle viscosity
structure and (c) a schematic diagram of the
numerical method that couples the 3-D-lithosphere–asthenosphere code SLIM3D
to a lower mantle spectral flow code at a
depth of 300 km. Panels (d) and (e) show the thermal
structure at a depth of 80 km from two 3-D thermal models adopted in this
study. (d) TM1, a heat flow-based thermal structure inferred from
the TC1 model of in the continents and the seafloor age
model of in the oceanic areas. (e) TM2, the
thermal structure of the upper mantle inferred from the S-wave tomography
model SL2013sv of . The “ringing” visible in
panel (d) is an artifact introduced by smoothing sharp boundaries
with a spherical harmonic expansion.
Results and discussion
Average creep viscosities and corresponding basal tractions
We follow the study of with estimates of global dynamic
geoid and plate motion velocity to test whether our prescribed lateral
viscosity variations within the upper mantle yield realistic results.
Together with the resulting shear tractions at a depth of 300 km, which
generate stresses in the lithosphere, results
are shown in
Fig. a–c. We compared our predicted geoid
(Fig. a) calculated with a 3-D viscosity structure
within the upper 300 km to the observation-based GRACE model
(see Supplement Fig. S2a) yielding a
correlation of 0.85 at spherical harmonic degrees l = 1–31. We also compared it
to the geoid estimate from the simulation using a layered/radial viscosity
structure for all depths (see Supplement
Fig. S2c) resulting in a somewhat lower correlation of 0.82.
In Fig. d, we show profiles of the estimated
effective creep viscosity for continents and oceans within the upper 300 km
using olivine parameters modified after (Shown in the
Appendix, Table ). Figure d
shows how a laterally averaged (dependent on depth only) asthenospheric
viscosity decreases with increasing water content (i.e., 100, 500, 1000
H/106Si). The viscosities are averaged separately across the continental
and oceanic regions (Fig. d, dashed versus solid
lines). The average oceanic viscosity profiles give lower values than the
respective average continental viscosity (ηeff), within the depth
range of 100 ± 60 km. Seismological studies e.g., show this as a seismic wave velocity drop
(∼ 5–10 %), and as a transition between the lithosphere and
asthenosphere corresponding to the low viscosity channel
(Fig. d). Figure d shows
tractions causing stresses and topography in the lithosphere from the
simulation using the creep parameters that correspond to the green effective
viscosity profile in Fig. d, which was used
to model the dynamic geoid and plate motions. Here, at all plate boundaries
we have used a friction coefficient μ=0.02 within the crust and
lithospheric layers to generate the global plate velocities in a
no-net-rotation (NNR) reference frame shown in
Fig. b with a RMS of 3.5 cm yr-1. Since the focus of
this study is to investigate the effect of the upper mantle lateral density
variations on the horizontal stress field and dynamic topography, an
assessment of the influence of the plate boundary friction and water content
in the asthenosphere on plate velocities has been carried out in a separate
study . In the present work, we therefore constrain our
resulting creep viscosity with a cutoff for extreme viscosity values in the
upper mantle by setting permissible minimum and maximum viscosity values
similar to and ; this approach
yields a good fit between the observed and modeled geoid.
Shallow and deep contributions to the crustal stress state
We start by examining the separate contributions of the mantle heterogeneities
below (deep Earth setup) and above (shallow Earth setup) 300 km to the global
lithospheric stress field and topography. To calculate the contribution of
the lower domain, we use a constant lithosphere thickness (100 km) and
density (3.27 kg m-3), with the same configuration of the mantle below as
was used to derive the geoid anomaly, plate motions and shear tractions in
Fig. a–c. The resulting maximum horizontal
magnitude (SHmax) and direction of the lithospheric stress field are
shown in Fig. a. We have obtained compressional regimes in
regions of past and present subduction. On the North and South American
continents, beneath which the ancient Farallon and Nazca plates were
subducted, compressive stress magnitudes reach about 40 MPa. In the Far East,
downwelling flows stretching from north to south from the northwestern
Pacific through Australia towards Antarctica create compressional stress
regimes with magnitudes ranging between ∼ 50 and 80 MPa. These
compressional regions are connecting the Arctic with Antarctica and engulf
two distinct regions with extensional stress regimes centered on the Pacific
and African superswell regions. The predicted SHmax directions in
Fig. a generally follow the first-order lithospheric
stress pattern (Zoback 1992), similar to previous mantle flow predictions of
lithospheric stresses .
In the largest extensional regions such as those found in the Pacific Superswell
and above deep upwellings across southeastern Africa, stresses reach
magnitudes of around 30 MPa. The modeled extensional/compressional patterns in
the constant lithosphere, which get smoothed out over large distances are
induced by the gradient in the tractions (Fig. c)
coming from the mantle flow.
(a) Model-based maximum horizontal stress magnitude and
most compressive stress directions [SHmax] following the convention
with compression being positive, originating from mantle flow driven by
density anomalies below 300 km. (b) Same for structure of the top
300 km of the upper mantle, computed with the CRUST 1.0 model and TM1
beneath air (free surface).
To investigate the contribution of the upper domain (300 km) to the stress
field, we calculate the magnitude and direction using model TM1
(Fig. d) combined with the CRUST 1.0 model
and disregard mantle density variations below 300 km (i.e.,
both horizontal and vertical tractions below the depth of 300 km are set to
zero). Comparison of the lithosphere stress predictions from our shallow
(Fig. a) and deep (Fig. b) Earth setups
reveals notable differences in the model-based stress regimes, magnitudes and
directions in continental regions. If stresses are generated by the upper
domain only, then almost all continental regions are characterized by an
extensional regime, with the largest stress magnitudes found in areas of high
topography and orogenic belts, such as the Tibetan and Andean highlands. Our
stress predictions from the shallow Earth setup with laterally varying
crustal and lithospheric densities in Fig. b show stress
magnitudes and patterns similar to . However, as opposed to
the results of we predict high compressional stress
magnitudes at continental margins, which may in part originate from a finer
treatment of the crust and our temperature-dependent creep viscosity. Also
the high compressional stresses along the subduction margins in
Fig. b are likely induced by the slab models included in
our setup. The resulting topography beneath air (free surface) accompanying
either modeled lithospheric stress field is shown in Supplement Fig. S3a–b.
Total lithospheric stresses and topography
Next we compute the combined effect of both the lower mantle buoyancy and the
upper mantle heterogeneities on the global SHmax magnitude and direction
for comparison with the separate contributions discussed above and with
observations. Note that this is not a linear superposition of the separate
contributions, because changes in the properties of the upper 300 km lead to
changes in the topography and stress caused by density anomalies below 300 km
depth. The resulting SHmax direction and magnitude
(Fig. a) due to the combined contributions of the upper and
lower mantle show compressional regimes in areas similar to
Fig. a, while muting almost all strong extensional
stresses predicted by our simulation with the shallow Earth setup in
continents (Fig. b). The predicted SHmax
orientation also generally follows the first-order lithospheric stress pattern
, similar to predictions based on only density anomalies
below the 300 km depth (Fig. a), with some regional
deviations. The dominance of the contribution from below 300 km to the
lithospheric stress field orientation becomes apparent when looking at the
similarities between the SHmax directions in Figs. a
and a and dissimilarities with Fig. b,
especially within continents. Nevertheless, the contribution from the upper 300 km to the predicted stress magnitude is evident in areas with large crustal
thickness in continents, such as Tibet and the Andes. The regions where
extensional regimes are predicted with only the contribution from below 300 km (Fig. a) correspond well with the extensional stress
regions in the combined model (Fig. a).
Predictions of the SHmax magnitude and direction from combined
contributions due to lower mantle flow and upper mantle from (a) TM1
with crust model and (b) TM2 with crust model beneath air (free
surface).
The result is not very different, when we use the thermal density model TM2
for the total lithospheric stress field prediction. Both the predicted
SHmax magnitude and direction with TM1 (Fig. a) and
TM2 (Fig. b) show notable similarities in oceans and
continents, owing to the strong contributions from below 300 km which are
similar for both models. They show relatively high compressional stress
magnitudes in subduction or convergence regions such as the Mediterranean,
south of the Tibetan Plateau, south of Alaska, and the northwest Pacific
extending through the Sumatra subduction zone and underneath the Australian
and Antarctic plates. However, the SHmax compressional signal underneath
North America in Fig. a is muted and that of the South
American region turns into an extensional regime along the Andes
(Fig. ) with the inclusion of the mantle above 300 km and
the crust. Similar to Fig. a both predictions with TM1
and TM2 (Fig. a and b) show SHmax
extensional regimes corresponding to the regions of upwellings and/or
volcanism. However, the model with TM2 generates a much higher extensional
magnitude of ∼ 60 MPa in the North Atlantic region around
Iceland, and around the Azores and Canary hotspots, compared to TM1. Stress
magnitudes are more alike in the southern Pacific Rise and around southern
Africa. Differences are in part due to the detailed and well resolved upper
mantle structures in the S-wave model used to derive TM2
, as opposed to the upper mantle structure in TM1, which
is based on the seafloor age in oceanic regions and slab
temperatures from . Also in regions where the coverage
of heat flow data is poor (e.g., in South America and Antarctica,
), TM2 (Fig. b) may give
better results. TM2 predicts compressional stress under Antarctica and along
the subducting Nazca Plate in South America induced by downwelling flow. In
these regions there are barely any heat flow data and TM1 remains largely
unconstrained. Both modeling setups with the combined effects from the
crustal structure model, the upper mantle thermal-density structure (either
TM or TM2) and deep mantle contributions give topography
(Fig. c–d) comparable to actual topography (see
Supplement Fig. S4a–b).
Lastly, we tested the bending of stresses inside plates with calculations in
which the effect of elasticity is set to zero. This was compared with
similar stress calculations considering elasticity and we found that
elasticity has greater influence on the modeled stress magnitude compared to
the corresponding orientations as given in Supplement Fig. S5. Bending stresses are less compressive in regions of continental margins and at
the foot of the Andes whereas they are extensional
above subduction zones for
example Izu–Bonin–Mariana (Supplement Fig. S5).
Modeled versus observed lithospheric stress field
We compare our predicted SHmax orientation to the observational stress
data. Following the stress interpolation method presented by
, we used their fixed search radius (FSR) method which uses
a global weighting defined by a fixed Euclidean distance for the stress data
interpolation and stress quality. The smoothed stress field orientation at a
grid point is based on the dominant stress data orientation within the
selected radius. For a detailed explanation on the FSR method see
. Stress data with quality A, B and C with known stress
regime were considered. Since we do not consider the respective regime in our
quantitative analysis, we also included the stress data with unknown style
having quality A and B in our smoothing procedure to make our smooth field
more robust. We smoothed the observed SHmax orientation of the World
Stress Map 2016 (WSM2016) , with a search radius of 270 km
(Fig. a) on a grid interval of 2.5∘ × 2.5∘. The background dot colors in the smoothed map represent the
stress data regimes with red denoting normal fault, blue as thrust fault,
green as strike-slip fault and black as unknown regime. For the interpolation
we only took the orientation pattern of the stress data into account. We
limit our comparison with modeled lithospheric stress orientation to areas
with enough data for interpolation. The new WSM2016 has a relatively good
coverage in some regions that were not well covered in the previous version
such as Brazil, parts of North America, eastern Russia,
and central Africa. We regard it as appropriate to compare the modeled stress
orientation with the smoothed observational stress data and regard deviations
of actual stress from smoothed stresses as a second-order pattern.
(a) Interpolated World Stress Map 2016 ,
data on a grid of 2.5∘ × 2.5∘, using only stress
orientation with a constant search radius 270 km, and (b) predicted
SHmax orientation and regime from total stress contribution with TM1
(plotted in thin bars) over TM2 (thick bars) upper mantle thermal structures.
Colors of dots (a) and bars (b) indicate observed or
predicted stress regime with red for normal faults or tensile stress, blue
for thrust faults or compressive stress and green for strike-slip faults or
intermediate stress (one principal horizontal stress positive, one
negative).
Angular misfit between WSM2016 and modeled lithospheric stress
In Fig. b we have superimposed our total
modeled stress fields resulting from TM1 depicted by thin bars on top of the
TM2 results as thick bars. There is relatively good agreement between the stress
patterns and regimes at a longer wavelength; however, the smaller-scale
contribution from the upper 300 km generate regional variations, which are mainly due to density contrasts in the
lithosphere or below (which are almost isostatically compensated or
cause lithosphere flexure) and topography . Compared to the observed SHmax patterns and regimes
(Fig. a) we predict similar styles in regions such as
eastern Africa and Tibet with normal faulting comparable to earlier works
that considered the effect of the whole mantle including lithosphere and
crustal models . We
predict normal faulting mostly in regions above upwellings (mostly
extensional regions) such as the Icelandic swell, eastern African Rift, or
along divergent plate boundaries, while thrust faults are mainly found in
compressional regions such as subduction zones and some other tectonically
active regions in continents.
Angular misfit between the observed (WSM 2016) and total modeled
stress directions with (a) TM1 and (b) TM2 upper mantle
thermal and density structures.
To further evaluate the influence of each thermal structure we performed a
quantitative comparison between modeled and smoothed observed stress
orientations. The angular misfit (Fig. ) is the minimum angle between the modeled lithospheric stress orientation
(Fig. b for TM1 and TM2) and smoothed observed stress
orientation (Fig. a), which ranges from 0 to
90∘. Here, an angular misfit lower than 22.5∘ is regarded as
representing a good agreement between the modeled and observed stress
orientations, with values above 67.5∘ regarded as indicative of a poor
fit. The general SSW to NNE stress orientation observed over the North
American Plate is matched by our model predictions with both thermal
structures TM1 and TM2. The angular misfit maps over North America obtained
with both thermal structures show a poor fit over Yellowstone and the Rocky
Mountains extending to the Great Plains . The observed
localized NW to SE stress direction deviates (Fig. a)
from the predicted long-wavelength stress pattern . Even though the thermal model TM2 includes high-density
cratonic roots, as opposed to TM1, their respective results for the angular
misfits show that the North American cratonic root has a limited influence on
the stress field. The two density structures TM1 and TM2 yield mean values of
22.2∘ (standard deviation, SD = 19.6∘) and 22.9∘ (SD = 20.7∘),
respectively. As the upper mantle thermal structure TM1 for the South
American continent is not well constrained, due to lack of heat flow data,
the predicted stress field in continental Brazil gives a relatively poor fit,
with a mean misfit of 37.73∘ (SD = 20.24∘). However, TM2 does
not perform much better resulting in a mean misfit of 33.79∘ (SD = 21.9∘). Both models fail to match the observed stress field in the
Andes, where dominant localized N–S orientation is predicted, mainly as a
results of the high topography and large crustal thickness compared to either
Fig. c or 8d without the crustal contribution or stress field
due to mantle below 300 km (Supplement Fig. S6a). In the
African continent, predicted N–S stress orientations along the eastern
African Rift from either model match the observed stress quite well with TM1
fitting observations much better compared to TM2 around the
Ethiopia–Somalia–Yemen region but both fail over the Congo craton and the
South African Plateau.
Regional comparison of the angular misfit in Europe (a, b)
and Australia (c, d) between the observed and modeled total stresses
with TM1 (a, c) and TM2 (b, d).
Red bars denote modeled orientations versus black bars showing the smoothed
observed stress field (WSM2016).
It has been suggested that the stress field in western Europe is influenced
by the North Atlantic Ridge (NAR) push in the west and possibly by the
far-field slab pull from the northwestern Pacific subduction zones, while in
the south, the driving forces are induced by the convergence of the African
and Eurasian plates, with Africa subducting under Eurasia in the
Mediterranean .
emphasize the importance of the anomalous mantle pressure
underneath the North Atlantic lithosphere for generating the dominant
first-order NW–SE stress pattern. In our study, due to mantle contribution
> 300 km, we could match the NW–SE stress orientation almost perfectly, with
the model using TM1 (Fig. a) showing small
regional deviations, while the use of TM2
(Fig. d) results in larger deviations from this
NW–SE pattern in some regions.
Modeled “dynamic” topography using the upper mantle structure
(a) TM1 and (b) TM2 and corresponding SHmax
prediction with (c) TM1 and (d) TM2. In contrast to
Fig. , the effect of the crust is not included here.
These regional pattern deviations between modeled and observed
orientations are mainly induced by differences in the upper mantle density
structures and topography (compared to
Fig. a). The high density of heat flow data
in continental western Europe (TM1) improves
the fit to the observed stress field compared to the thermal structure based
on S-wave velocity (TM2) yielding mean misfit values of 18.30∘ (SD = 22.67∘) and 19.9∘ (SD = 22.64∘), respectively.
Similarly, the large amount of heat flow data in the Australian continent,
improves the fit of the predicted intra-plate stress to the WSM2016
(Fig. c, mean = 23.07∘ and SD = 19.4∘) compared to TM2 (Fig. e,
mean = 32.7∘ and SD = 24.22∘). It has been argued that the stress
pattern in Australia is mainly driven by plate boundary forces
, but based on the lithospheric and crustal structures used
we show here that crustal and sub-lithospheric heterogeneities have a certain
degree of influence.
In the Tibetan region, the collision of India and
Eurasia leads to a complex crustal and lithospheric deformation
generating NE–SW compressional stresses. The
SHmax predictions with TM1 (Fig. c) fit
better the stress pattern over the Tibetan Plateau with a mean misfit value
of 28∘ (SD = 23∘) compared to TM2, where a predicted E–W
direction results in a misfit of ∼ 50∘
(Fig. f). Both models perform relatively poorly
over parts of China, when compared to the observed stress field. The comparatively large
angular misfit from the modeled stress field with only crustal and mantle
contributions
above the 300 km shows how much stress field is influenced by the
mantle below (Supplement Fig. S6b). This is also supported by the
fact that considering different thermal structures and/or correcting for the
continental depletion does not seem to significantly improve the pattern of
angular misfits (Supplement Fig. S7a–c).
Modeled “dynamic” topography
Following the above prediction of lithospheric stress field, we repeated the
two simulations to compute the topography, but this time without crustal
thickness variations (Fig. a–b) to distinguish isostatic
contributions from non-isostatic contributions. The corresponding stress
magnitude and orientation from TM1 (Fig. c) and TM2
(Fig. d) without the crustal contribution are quite similar
to the respective previous results that include the crustal contribution but
show some regional differences, such as the N–S predicted stress orientation
in the Andes in Fig. a–b compared to
Fig. c–d. Here, the resulting topographies with TM1
(Fig. a) and TM2 (Fig. b) show similar
amplitudes due to the seafloor cooling and thickening along the ridges in
the Atlantic, Indian and Pacific oceans, peaking above ∼ 1.5 km. With TM1, which explicitly contains subducted slabs, narrow, deep
trenches are computed above subduction zones, such as in the northwestern
Pacific and at the west coast of South America. Also the negative topography
in the plate boundary south of Indonesia is reproduced well with the TM1 model reaching
a value ∼ -1.8 km. Based on tomography (model TM2) the
computed topographic lows are wider and less prominent.
Predicted topography with TM2 is higher in eastern Africa (2 to 2.5 km), and
highly elevated regions are more extensive. Figure a with TM1
(based on seafloor age) shows relatively low topography amplitudes in the
northwest of the Pacific Plate around Hawaii and towards the Mariana Trench
compared to Fig. b with TM2 (based on the S-wave model
SL2013sv) corresponding to a mean regional temperature difference of about
∼ 200 ∘C between TM1 and TM2 (Fig. d–e).
The “dynamic” topography with TM2 replicates nearly all island chains
associated with hotspots in and around the African Plate, in the Pacific and
along the Atlantic opening. In the North Atlantic, the positive topography
(Icelandic swell) due to the Iceland plume–lithosphere interaction
is more pronounced in Fig. b
with TM2 based on the tomography of . Here the heights
exceed 2 km as compared to Fig. a with TM1 based on the
ocean floor ages of , showing values slightly below 2 km.
The high isostatic topographic amplitudes along the mid-ocean ridges (MORs)
as a result of high temperatures beneath these spreading centers where new
seafloor is created are generally more pronounced in the TM2 model simulation
than in the TM1 experiment. Despite the striking differences between
topographic amplitudes in Fig. a and b along the MORs, the
resulting modeled stress orientations (Fig. c–d) are very
similar in these regions.
Also the large negative topography amplitude in cratons observed in dynamic
topography with TM2 compared to TM1 does not readily translate into similarly
large variations in the respective predicted SHmax orientation
(Fig. c–d), showing that cratonic roots have less influence
on the lithospheric stress field . Low temperatures as
shown in the thermal model TM2 (Fig. b) translate into strong
negative topographic anomalies, which are due to the conversion from seismic
models to temperature and density, with the assumption that all seismic
velocity anomalies are due to thermal variations only. This produces
unrealistically strong density anomalies and hence, large negative topography
in cratons , if correction due to the chemical depletion in
the mantle lithosphere is not considered. Previous studies of cratonic mantle
depletion in relation to density and temperature inferred from S-wave models
(for example, ) identified composition as the key dominant
agent for the low-amplitude topography. They showed that a 100 K hotter
mantle combined with lateral variations in composition resulted in a density
of about 0.1 g cm-3 lower compared to models assuming pyrolitic
composition. In contrast, found that the depletion-related
density drop in cratons is age-dependent and increases from 30 to 80 g cm-3 (i.e., 0.03 to 0.08 g cm-3) for Phanerozoic through Protozoic
to Archean platforms. Here we aim at a qualitative first order analysis and
therefore apply a density drop of 0.04 g cm-3 (modeled as an equivalent
temperature increase of about 300 K) as correction in TM2 cratons. Also,
following the realistic compositional correction in cratons by
we adopt two additional thermal structures from different
seismic tomography models SAW24B16 and S20RTS
with corrections applied to the depleted mantle based on
the thermodynamic model PerpleX (http://www.perplex.ethz.ch, last access: 15 July 2017; )
(See Supplement Fig. S8a–b) and compare with our results.
Comparing (a) the in situ observed residual topography from
, and (b) the residual topography based on the
CRUST 1.0 from with modeled dynamic topography using
TM1 (c) and TM2 (d) upper mantle thermal density structures
with the effect of seafloor cooling with age removed.
(e) Similar modeled dynamic topography using TM2 upper mantle
thermal density structures with constant temperature (300 K) added in
cratons. Green dots with black circles around them show locations of major
hotspots .
Comparing the modeled dynamic topography to the observation-based residual topography
Here, we compare our modeled dynamic topography to two independent
observation-based residual topography fields . Residual topography gives a convenient way to constrain both
isostatic and non-isostatic contributions to the modeled dynamic topography
.
This is done with the assumption that if topography is perfectly compensated
isostatically within the upper mantle at depths within the range of 100–150 km, the integral of density with depth, as a function of crustal thickness
and density to the Moho depth and of seafloor age will be the same
everywhere for the chosen depth. The observation-based model by
is derived from ocean seismic surveys (in situ) in oceanic
regions and free-air gravity anomaly data in continents
(Fig. a), while the residual topography model
of (Fig. b) is derived
with the CRUST 1.0 model . These two models are comparable in
most oceanic regions, but give large mismatches in continents. For example,
the subducting plate under South America induces a negative anomaly in
Fig. b but in the same region there is a
positive anomaly in Fig. a due to the
free-air gravity data used across continents. Hence, we perform a regional
quantitative comparison for oceans and continents separately. To compare the
modeled dynamic topography from TM1 and TM2 simulations
(Fig. a and b) to the observation-based fields
(Fig. a and b),
we first remove the height due to ocean floor cooling. This is done by
subtracting the height estimates from seafloor age from
the modeled dynamic topography, using the relation Htopo = 3300 m × (1-age100Ma). Here we assume a half-space cooling for the sea
floor with age. For a smooth transition of topographic height from ocean to
continent and to avoid large jumps we nominally assume a 200 Ma lithosphere
age for continents following the approach of . The
resulting modeled dynamic topography fields
(Fig. c–d) corrected for the effect of the seafloor
cooling with age with locations of active hotspot volcanism
plotted as green dots show to which extent each of the
models is able to predict the positive topographic amplitudes due to
upwellings induced by plume heads pushing the lithospheric base.
A visual comparison of the two observation-based residual topography fields
(Fig. a–b) with the modeled topography
(Fig. c–d) shows some features that are well
reproduced such as the Pacific swell and the Hawaiian plume track, while the
Canary Island plume, and the heights around southeastern Africa are much
better reproduced by the TM2-based dynamic
topography (Fig. d). Removing the height due to
ocean floor age results in either zero or negative topographic amplitudes
along MORs in the Atlantic and Indian oceans in the TM1-based dynamic
topography (Fig. c), giving correlation of
0.323 and 0.198 (Table ) in oceans to
(S2016) and (H2016), respectively. This
model uses the thermal density structure derived from the ocean floor age in
the upper 300 km; hence, when this contribution is removed, only the lower
mantle contribution remains. In contrast, the TM2 model still gives
small-scale topography anomalies (Fig. d) due
to density anomalies other than from the seafloor cooling at depths above
(300 km), which are resolved by the seismic model used to derive TM2, thereby
giving relatively higher correlation with S2016 and H2016 of 0.348 and 0.284 in
oceans, respectively. To estimate the separate regional ratio between the
modeled and observation-based residual topographies for continents and
oceans, we assigned the continental mean value in continental areas to
estimate the degree by degree ratio for oceans only (Fig. b)
and vice versa for oceanic regions to estimate continents ratio
(Fig. a).
Correlation between the modeled dynamic topography and the
observation-based residual topography models
for continents and oceans.
Modeled topography
()
Upper mantle thermal density
Ocean
Continent
Ocean
Continent
1. TM1
0.323
0.481
0.198
0.169
2. TM2
0.348
0.498
0.284
0.171
3. TM2 + 300 K (in cratons)
0.370
0.500
0.284
0.192
4. S20RTS
0.442
0.653
0.221
0.232
5. SAW24B16
0.248
0.718
0.287
0.188
Ratio of modeled dynamic topography from TM1, TM2, SAW24B16 and
S20RTS for (a) continental and (b) oceanic regions with
observation-based residual topography from and
.
In continents, the TM1 model (Fig. c) is
similar to the residual models (Fig. b),
exhibiting a correlation of 0.481 and a ratio of 0.98
(Fig. a) up to the spherical harmonic degree 30. The TM2
model gives similar ratio and correlation, but at degrees lower than 15 the
TM2-induced modeled dynamic topography is about twice the amplitude of TM1
(Fig. a). Over the African continent with far less heat flow
data used to derive TM1, this thermal density structure gives a large
continental uplift up to about 2 km, similar to parts of Antarctica
(Fig. c). In
TM2 (Fig. d) this uplift is less extended, better
resolving the negative topography of the Congo craton but reaching a height
above 2 km over the East African swell similar to S2016
(Fig. b). Many of the remaining continental
regions, however, show large negative topographic magnitudes of -2 km and
more, resulting from neglecting the compositional effects in cratons (e.g.,
Eurasia, Australia and North America). The wide range of variations shown in
degree 1 to 2 ratio for continents (Fig. a) is due to the
strong contributions coming from the different cratonic structures in each
thermal model. To further evaluate the impact of accounting for the
correction due to chemical depletion in cratonic regions on the stress field
and the dynamic topography, we have assumed an additional 300 K converted to a
negative density as a compositional contribution in all cratons to the depth of
100 km for TM2; this is as opposed to the more realistic treatment of compositional
effects as done for SAW24B16 and S20RTS, with the method from
. The modeled topography shows improvements in cratonic
regions but there is almost no change in the resulting lithospheric stress
field (Supplement Fig. S8c). The correlation with S2016
increases to 0.512 for TM2 (with an assumed 300 K compositional effect) in
continents. SAW24B16 and S20RTS give much higher correlation 0.653 and 0.718
in continents (Table ), which could be the result of a more
realistic treatment of cratonic regions but also of using different seismic
tomography models. , for example, used a similar simple
procedure to convert seismic velocities from different tomography models to
density and still obtained a rather high correlation of 0.64 in continents.
The assumed compositional correction is not very large giving about a 100 m
reduction in the cratonic negative anomaly
(Fig. e) compared to the case without
correction in continents (Fig. d). This in
part supports the proposed treatment of the upper mantle thermal density
structure with joint petrological and seismological constraints
, which is outside the scope of our
studies. The residual topography of shows positive
amplitudes over the Eurasian craton due to the free-air gravity data used,
while the other residual (Fig. b) and all
modeled dynamic topography models give negative values, resulting in a low
correlation with H2016 on continents for all models.
Conclusions
The aim of our study is to identify and quantify the influence of density
anomalies and rheology in the crust and mantle on the present-day
lithospheric stress field and dynamic topography. The focus is on anomalies
and rheology above 300 km depth; therefore we use a number of different
density structures, and nonlinear temperature and stress dependent rheology
above 300 km. Our first upper mantle thermal-density model (TM1) is based on
heat flow data on continents and seafloor age
in the oceans; while the upper mantle second
thermal-density model TM2, and several alternative models considered, are
based on seismic tomography . In
contrast, only one density structure, based on the SMEAN (Becker and Boschi,
2002) tomography, and a radial viscosity structure is
used below 300 km depth. A key feature that distinguishes our work from
previous studies is the use of a coupled code that
considers density heterogeneity in the entire mantle, along with a realistic
lithosphere with free surface, such that lithosphere stresses are computed
with a fully three-dimensional, rather than a thin-sheet approach.
Resulting lithosphere stresses are rather similar, both among the different
models we consider, and to previously published results. They are also
similar to the case where only the contribution from the mantle below 300 km is
considered, showing that a larger portion of the contribution to the
lithospheric stress field originates from mantle flow driven by density
anomalies below 300 km depth .
Only in some regions, particularly those with large and variable crustal
thickness, such as Tibet, or the Altiplano, shallow contributions are
dominant. A lower mantle stress contribution is dominated by
very large-scale structures, with stress directions remaining similar over
thousands of kilometers. It is related to very large scale mantle structures,
which are well imaged by seismic tomography, causing overall similarity
between our models and published ones. However, the modeled stress magnitudes
coming from the mantle below 300 km or the total contributions (i.e., crust,
lithosphere and the mantle below 300 km), are influenced by the respective
density structures.
We compare computed directions of maximum compressive stress with the World
Stress Map, and find a rather good overall agreement, confirming previous
comparisons. However, regional comparison highlights those areas where the
fit remains poor: these include the Colorado Plateau, the Altiplano, parts of
Brazil, the Congo craton, and parts of China, highlighting regions on
which future studies could focus. Computed stresses based on heat flow (Model
TM1) compare more favorably to observations in those regions where heat flow
coverage is good (e.g., western Europe), whereas the stresses computed from
tomography (Model TM2) give a better fit for regions of poor heat flow
coverage, such as South America.
In contrast to stress field, density anomalies above 300 km depth contribute
dominantly to dynamic topography. Therefore, dynamic topography is more
variable among the different models we consider and differs more strongly
from published models. Dynamic topography also has a larger contribution at
smaller scales. Some of these contributions can be related to subducted slabs
or mantle plumes. Confirming previous results, we find that negative
topography in cratons is too large, unless a correction for the depletion of
cratonic lithosphere is considered. The best fit can be obtained, if the
method of is used to convert seismic tomography models to
temperature structures, taking chemical depletion in cratonic areas into
account. The best agreement is found with residual topography on continents
that considers crustal thickness variations based on CRUST1.0
rather than deriving it from the gravity field. In order to fit either
observable (stress or topography) attention has to be mostly paid to a
detailed treatment of the Earth's parts (deeper or shallower) that give
the largest contribution.