The orientation and tectonic regime of the observed
crustal/lithospheric stress field contribute to our knowledge of different
deformation processes occurring within the Earth's crust and lithosphere. In
this study, we analyze the influence of the thermal and density structure of
the upper mantle on the lithospheric stress field and topography. We use a 3-D
lithosphere–asthenosphere numerical model with power-law rheology, coupled to
a spectral mantle flow code at 300 km depth. Our results are validated
against the World Stress Map 2016 (WSM2016) and the observation-based
residual topography. We derive the upper mantle thermal structure from either
a heat flow model combined with a seafloor age model (TM1) or a global
S-wave velocity model (TM2). We show that lateral density heterogeneities in
the upper 300 km have a limited influence on the modeled horizontal stress
field as opposed to the resulting dynamic topography that appears more
sensitive to such heterogeneities. The modeled stress field directions, using
only the mantle heterogeneities below 300 km, are not perturbed much when the
effects of lithosphere and crust above 300 km are added. In contrast, modeled
stress magnitudes and dynamic topography are to a greater extent controlled
by the upper mantle density structure. After correction for the chemical
depletion of continents, the TM2 model leads to a much better fit with the
observed residual topography giving a good correlation of 0.51 in continents,
but this correction leads to no significant improvement of the fit between
the WSM2016 and the resulting lithosphere stresses. In continental regions
with abundant heat flow data, TM1 results in relatively small angular
misfits. For example, in western Europe the misfit between the modeled and
observation-based stress is 18.3

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

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

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

Also, constraining the modeled lithospheric stress with observations is
challenging due to previously poor spatial coverage by World Stress Map
data

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,

Adopted from

Our global numerical model of the Earth interior consists of the
particle-in-cell finite element model SLIM3D

This study complements our previous study

We assign densities of the uppermost layers according to the crustal model
CRUST1.0

We follow the study of

In Fig.

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

To investigate the contribution of the upper domain (300 km) to the stress
field, we calculate the magnitude and direction using model TM1
(Fig.

Next we compute the combined effect of both the lower mantle buoyancy and the
upper mantle heterogeneities on the global SH

Predictions of the SH

The result is not very different, when we use the thermal density model TM2
for the total lithospheric stress field prediction. Both the predicted
SH

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).

We compare our predicted SH

In Fig.

Angular misfit between the observed (WSM 2016) and total modeled
stress directions with

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.

Regional comparison of the angular misfit in Europe

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

Modeled “dynamic” topography using the upper mantle structure

These regional pattern deviations between modeled and observed
orientations are mainly induced by differences in the upper mantle density
structures and topography

In the Tibetan region, the collision of India and
Eurasia leads to a complex crustal and lithospheric deformation

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.

Predicted topography with TM2 is higher in eastern Africa (2 to 2.5 km), and
highly elevated regions are more extensive. Figure

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 SH

Comparing

Here, we compare our modeled dynamic topography to two independent
observation-based residual topography fields

A visual comparison of the two observation-based residual topography fields
(Fig.

Correlation between the modeled dynamic topography and the
observation-based residual topography models

Ratio of modeled dynamic topography from TM1, TM2, SAW24B16 and
S20RTS for

In continents, the TM1 model (Fig.

The assumed compositional correction is not very large giving about a 100 m
reduction in the cratonic negative anomaly
(Fig.

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

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

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

The coupled global numerical code used to generate the
results in this study builds on an in-house SLIM3D code

The coupling between the lithosphere and the mantle in our model allows for
an implementation of realistic rheological parameters in both model domains.
In SLIM3D, the stress- and temperature-dependent rheology is implemented
according to an additive strain rate decomposition into the viscous, elastic
and plastic components:

Along plate boundaries we account for the brittle deformation, with the yield
stress defined according to the Drucker–Prager criterion based on the dynamic
pressure:

The upper mantle creep viscosity is
calculated using olivine parameters from the axial compression experiments of

The authors declare that they have no conflict of interest.

This work was supported by GeoSim Grants under the Geo.X program in conjunction with GFZ-Potsdam, University of Potsdam, Free University of Berlin, and the BNBF project pacMod. Lastly, we thank the anonymous reviewer and the editor, Taras Gerya, for the constructive comments to improve our manuscript. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Taras Gerya Reviewed by: one anonymous referee