Understanding the long-term evolution of Earth's plate–mantle
system is reliant on absolute plate motion models in a mantle reference
frame, but such models are both difficult to construct and controversial. We
present a tectonic-rules-based optimization approach to construct a plate
motion model in a mantle reference frame covering the last billion years and
use it as a constraint for mantle flow models. Our plate motion model
results in net lithospheric rotation consistently below 0.25
The study of plate tectonics unifies our understanding of the evolving solid Earth, the ocean basins, landscapes, and the evolution of life. Since the advent of plate tectonic theory enormous progress has been made in mapping the relative motions of the plates through time, constrained by magnetic anomaly and fracture zone data in the ocean basins and a variety of geological, geophysical, and paleomagnetic data on the continents (see summary by Cox and Hart, 2009). Nonetheless, absolute plate motions, i.e. the motions of the plates relative to a fixed reference system such as the spin axis of the Earth or the mesosphere, have been much more difficult to constrain. Both the paleo-latitude of a plate and its paleo-meridian orientation can be calculated using paleomagnetic data, providing a paleomagnetic pole for a given plate (Cox and Hart, 2009). However, since the Earth's magnetic dipole field is radially symmetric, paleo-longitudinal information cannot be determined from paleomagnetic data alone unless further assumptions are made (Torsvik and Cocks, 2019). For relatively recent geological times (Late Cretaceous to present), seamount chains as well as continental volcanic formations with a linear age progression can be used to restore plates to their paleo-positions (including paleo-latitude and paleo-longitude), with the assumption that surface hotspots resulting from intersections of mantle plumes with the surface are either fixed relative to each other or moving slowly with respect to each other (Koppers et al., 2021). Various alternative time-dependent regional and global absolute plate motion models based on hotspot tracks have been developed over the past decades, with some based on hotspot track data alone (e.g. Maher et al., 2015; Wessel and Kroenke, 2008), while others reflect a combination of relative plate motion and constraints provided by mantle convection models (e.g. O'Neill et al., 2005; Steinberger, 2000). Hotspot-track-based models for recent geological times can be combined with models based on paleomagnetic data for earlier times, forming “hybrid models” (Torsvik et al., 2008). The difficulties involved in constructing hotspot reference frames, and their lack of robustness for pre-Cretaceous times, reflecting a shortage of preserved age-dated hotspot tracks, led to the idea of a subduction reference frame. This follows the assumption that slabs sink vertically through the entire mantle, allowing the location of past subduction zones to be reconstructed based on global mantle tomographic models (Van Der Meer et al., 2010). However, the empirical “longitudinal correction” applied to the plates in such models differs significantly with plate positions derived from hotspot track data (Butterworth et al., 2014). Domeier et al. (2016) tested the concept of a subduction reference frame concept using a range of tomographic models and concluded that the method may be used for reconstructions back to 130 Ma, reflecting imaged slabs down to a depth of 2300 km.
Considering that neither age-progressive hotspot tracks nor subducted slabs are useful for reconstructing the past positions of plates before the Cretaceous Period and the considerable challenge of reconstructing paleo-longitude from paleomagnetic data, Torsvik and Cocks (2019) built on the idea of large low-shear-velocity province (LLSVP) stability put forward in Burke and Torsvik (2004). LLSVPs were regarded as useful in this context as their edges were proposed to act as “plume generation zones”, offering an avenue to align age-dated large igneous provinces (LIPs) and kimberlites with the present-day edges of LLSVPs. This hypothesis is built on the assumption that LIPs and kimberlites are the product of plumes rising from LLSVP boundaries, which remain stationary through time (Burke and Torsvik, 2004).
However, using statistical approaches a number of studies (e.g. Austermann et al., 2014; Davies et al., 2015a) have shown that this correlation is not robust, whilst a follow-up study by Doubrovine et al. (2016) essentially confirms this in the sense that one cannot conclusively state that plumes form at LLSVP edges versus interiors. Using similar statistical approaches, Flament et al. (2022) recently showed that the alignment of LIPs and kimberlites is statistically as consistent with the boundaries and interiors of mobile basal mantle structures shaped by Earth's reconstructed subduction history as with fixed ones.
This plume generation zone method offers a reproducible and quantifiable method of adding a longitudinal correction to reconstructed plates, thus providing an apparent solution to reconstructing longitude. Le Pichon et al. (2019) also built an absolute reference frame based on an assumption of stationary deep mantle structures back to 400 Ma. However, the basic tenet of these approaches, namely the long-term stability of LLSVPs, has been challenged. Recent mantle tomographic images, combined with fluid mechanic constraints, have resulted in a view that LLSVPs are composed of bundles of thermochemical upwellings enriched in denser than average material (Davaille and Romanowicz, 2020), an interpretation that follows numerous previous papers coming to similar conclusions (e.g. Garnero and Mcnamara, 2008; Heyn et al., 2018; Tan et al., 2011). Only when tomographic models are filtered to long wavelengths do these structures take on the appearance of homogenous, uniform, and potentially stable provinces (see also Schuberth et al., 2009; Tkalčić et al., 2015). These models and observations, as well as mantle flow models (e.g. Zhang et al., 2010; Zhong and Liu, 2016; Cao et al., 2021a; Davies et al., 2015a; Garnero and Mcnamara, 2008; Flament et al., 2017; Bull et al., 2014; Davies et al., 2012), indicate that the shape of LLSVPs is controlled by the distribution of subducted slabs and the position of LLSVPs relative to them, implying that LLSVP structures and their boundaries are mobile. Based on mantle flow models, Zhang et al. (2010) concluded that the African LLSVP is unlikely to have existed in its current form before 230 Ma, while Mitchell et al. (2012) suggested, based on distribution patterns of virtual geomagnetic poles, that neither the African nor the Pacific antipodal upwellings existed before the creation of Pangea. Additionally, Doucet et al. (2020b) used the geochemical composition of plume-related basalts to argue for a dynamic relationship between deep mantle structures and plate tectonic evolution. These inferences remain to be further tested, but the apparent unlikelihood of LLSVP stability over long geological time periods challenges the usefulness of the method proposed by Torsvik and Cocks (2019) as a universal solution for reconstructing the longitude of plates.
Possible alternative modes of supercontinent formation include (1) closing
of the youngest ocean basin on the same hemisphere as the last
supercontinent (“introversion”, re-closing the Atlantic Ocean from the
present configuration), (2) closing of the older antipodal ocean basin
(“extroversion”, closing the Pacific Ocean from the present configuration),
and (3) closing an ocean basin orthogonal to the direction of opening of the
last ocean basin (“orthoversion”, e.g. closing the Arctic Ocean from the
present configuration) (Evans et al., 2016; Murphy and Nance, 2003;
Murphy et al., 2009). Following these ideas, Mitchell et al. (2012)
proposed an alternative method to obtain paleo-longitude from paleomagnetic
data across supercontinent cycles. They utilized the record of oscillatory
true polar wander (TPW) as expressed in apparent polar wander paths. True
polar wander is a solid-body rotation of the Earth about the equatorial
minimum moment of inertia with respect to its spin axis, causing geographic
poles to “wander” (Raub et al., 2007). Mitchell et al. (2012)
suggested that consecutive supercontinents are roughly separated from each
other by 90
The net rotation of the lithospheric shell of the Earth relative to the
underlying mantle owes its origin to lateral variations in upper mantle
viscosity and mantle structure (Rudolph and Zhong, 2014; Ricard et al.,
1991). Many published absolute plate motion models suffer from plate
velocity artefacts, typically resulting in excessive net lithospheric
rotation magnitudes. Often, absolute plate motion models are based on
fitting geological observations, which in some instances result in either the
over-fitting of observations or fitting the wrong trends within data from
volcanic chains (see Schellart et al., 2008, for a discussion),
resulting in geodynamically problematic models that are
difficult to reconcile with our knowledge of mantle rheology (e.g.
Rudolph and Zhong, 2014). As a consequence, mantle flow modellers often
convert a plate tectonic model into a so-called no-net-rotation (NNR)
reference frame (e.g. Mao and Zhong, 2021), in which the net rotation
of the entire lithosphere relative to the mantle is set to zero at all
times. Upper magnitude limits to net lithospheric rotation have been
proposed based on mantle flow modelling, suggesting net rotation should be a
positive, non-zero value less than
All absolute reference frames discussed above fall in the category of mantle reference frames, i.e. they are designed to estimate the position of plates relative to the mantle through time, as opposed to the spin axis. Unlike the spin axis, the convecting mantle does not provide a stable, fixed reference system through time. A mantle reference frame attempts to isolate the motions of plates relative to the mantle, given as plate rotations relative to the Earth's spin axis, which is assumed to be fixed. Such a reference frame is therefore agnostic of TPW. Paleomagnetic data record information informing both the motions of the plates relative to the mantle and TPW, and they can thus be used to restore the plates in terms of their “true” latitudinal positions through time, which is useful for paleoclimate studies. However, reconstructed paleomagnetic poles derived from paleomagnetic data cannot constrain paleo-longitude due to the radial symmetry of the Earth's magnetic field (Cox and Hart, 2009) and therefore cannot be used to accurately track the east–west movement of the plates across mantle upwellings and downwellings unless additional assumptions are made – see Sect. 1.2 in Torsvik and Cocks (2019). In contrast, an ideal mantle reference frame provides constraints on both paleo-latitudes and paleo-longitudes of plates relative to the mantle. However, as it does not consider TPW, it does not provide paleogeographic reconstructions useful for paleoclimate studies (Van Hinsbergen et al., 2015). These two types of reference frames are complementary to each other.
To overcome the limitations of traditional mantle reference frames, Tetley et al. (2019) presented a new method applying a joint global inversion to evaluate the contribution of multiple time-dependent absolute plate motion constraints including fit to age-progressive hotspot tracks, optimizing subduction zone migration behaviours, and minimizing rates of net lithospheric rotation. This approach explicitly excludes true polar wander, as the method is deliberately aimed at reconstructing the plates relative to the convecting mantle. The method automatically provides both paleo-latitudes and paleo-longitudes relative to the mantle, thus providing a mantle reference frame expressed as rotations of the plates relative to the spin axis of the Earth, which is assumed to be stationary. This approach has been extended for the application in this paper by including evaluation of continental velocities relative to the mantle as an additional criterion. Tectonic-rules-based plate motion model optimization can be applied to any plate motion model with continuous closing plate boundaries through time (Gurnis et al., 2012).
Our aim is to derive a mantle reference frame for the plate motion model of Merdith et al. (2021), extending the tectonic-rules-based approach proposed by Tetley et al. (2019) to the last billion years. This results in a “deep-time” plate motion model suitable for plate–mantle system simulations and allows us to test the orthoversion hypothesis suggested by Mitchell et al. (2012) independently of any reliance on paleomagnetic data. It also allows us to evaluate the difference between the widely used NNR reference frame approach and a more complex application of tectonic rules to reference frame construction, aiming to minimize net rotation jointly with other key parameters. Lastly, it allows us to design a plate–mantle system model to understand how the deep mantle structure responds to plate motions following a set of tectonic rules. For instance, we can test the hypothesis by Mitchell et al. (2012) that the African and Pacific LLSVPs did not exist before Pangea assembled.
It needs to be stated in the outset that prior to the assembly of Pangea we have far fewer constraints on the relative positions of plates compared to more recent times. To render mantle reference frame construction tractable, we leave relative plate motions unaltered and focus on optimizing a single, global reference frame. Our workflow for absolute plate motion model construction follows the iterative method outlined in Tetley et al. (2019) (Fig. 1). For a given iteration, the approach starts with perturbing an initial absolute Euler rotation (pole latitude, pole longitude, and angle magnitude) for a given reference continent or plate and then calculates a series of fit metrics with selected constraining data using objective (or cost) functions. This process continues until a global minimum is found. For this study, we use continental Africa as the reference (as it forms the base of the plate model rotation tree of Merdith et al., 2021). Following Tetley et al. (2019), we calculate fit metrics computed from evaluating (1) net lithospheric rotation rate (NR), (2) trench migration rate (TM), and (3) the fit of present-day hotspots to the major age-progressive hotspot tracks for the period of 0–80 Ma only (HS). In addition to the above, we extend the existing method to also compute a fourth constraining criterion: (4) median global continental absolute plate velocity (PV). We introduce continental absolute plate velocities as an additional criterion to prevent mean oceanic plate velocities based on synthetic plates from potentially inducing unreasonably high continental speeds globally, as the deep-time reconstructions used here include large swathes of reconstructed ocean floor that is now subducted based on a variety of indirect pieces of geological evidence (Merdith et al., 2021).
The four constraining criteria are applied to the absolute plate motion
model optimization with the following assumptions and/or bounds: (1) rates of net
lithospheric rotation (NR) are minimized but non-zero, (2) global trench
migration velocities are minimized, favouring trench retreat over trench
advance, (3) spatio-temporal misfit between the plate motion model and
present-day hotspot chains is minimized, and (4) global continental median
plate speed remains
Optimization workflow including decisions (yellow diamonds) and
directing flow through processes (rectangular grey boxes) that accept input
and produce output data (orange boxes). The beginning and end of the
workflow are denoted by light blue boxes with rounded edges. The workflow
sequentially optimizes absolute plate motion in 5 Myr time intervals
starting at present day and progressing backwards in time until 1000 Ma.
Within each time interval the motion of a reference plate (and thereby the
absolute motion of all plates) is optimized by perturbing its rotation while
iteratively minimizing the cost of an objective function. The reference
plate is Africa between 550 and 0 Ma and Laurentia between 1000 and 550 Ma. Global
optimization in the current time interval is initiated by generating 400 rotations with which to seed local optimizations. Each seed is generated
from the reference plate rotation optimized in the preceding time interval
by retaining its rotation angle but distributing its rotation pole (latitude
and longitude) to 400 uniform locations across the globe. To take advantage
of parallel processing we distribute these 400 seeds in parallel across
multiple computational nodes, with each node performing a local optimization
of a single seed, with the results from all nodes gathered to find the
globally minimal reference plate rotation for the current time interval. The
objective function (minimized during optimization) consists of four separate
weighted cost functions using the perturbed rotation model as input: (1) misfit distances of hotspot trails (between 0 and 80 Ma), (2) net rotation of
reference plate with an extra penalty if below 0.08 or above 0.20
We model mantle convection using the extended Boussinesq approximation in a
version of CitcomS (Zhong et al., 2008) which has been modified for
progressive assimilation of surface boundary conditions from plate
reconstructions (Bower et al., 2015). We build the thermal
structure of the lithosphere using reconstructed seafloor ages and a
half-space cooling model with maximum seafloor age set to 80 Myr. This
corresponds to a fast and simple implementation of the equivalent of a plate
model; for the purpose of our application, the difference to using an actual
plate model would be negligible. Similarly, we build the thermal structure
of subducting slabs from the surface to 350 km depth with a dip angle of
45
We consider four mantle model cases: cases OPT1 and OPT2 use our optimized
reconstruction as time-dependent boundary conditions, case PMAG uses the
reconstruction from Merdith et al. (2021), which is in a paleomagnetic
reference frame, and case NNR uses the same reconstruction except with net
lithospheric rotations removed (i.e. a no-net-rotation reference frame).
The initial condition includes a 113 km thick denser basal layer. The excess
density is defined by the buoyancy ratio
Parameters for mantle flow models.
The convective vigour is controlled by the Rayleigh number:
We follow the approach of Flament et al. (2022) to evaluate model
success from (i) the time-dependent match between volcanic eruption
locations and basal mantle structures and (ii) the match between the
present-day mantle structure predicted by mantle flow models and imaged by
tomographic models. We are primarily interested in basal mantle structures
(BMSs) that are hot in mantle flow models and slow in tomographic models.
The first step consists of carrying out a cluster analysis of lower mantle
structure. As in Flament et al. (2017), we classify
The first is the fractional area
The second is the accuracy Acc
The third is the time-averaged median angular distance
The last is the statistical significance of the median distance between volcanic
eruptions and BMSs, expressed as a fraction
Number of volcanic eruptions as a function of age from 0–960 Ma for databases EY17 (Ernst and Youbi, 2017), J18 (Johansson et al., 2018), and T18 (Tappe et al., 2018). The number of volcanic eruptions from 960 Ma is given in brackets for each database, as is the total number of volcanic eruptions.
To facilitate an objective, quantitative comparison between 3D volumes of
seismic velocity and model temperature fields in the lower mantle, we reduce
these 3D volumes into 2D maps using vertical volume averaging (see
Flament, 2019; Lekic et al., 2012). We use
In order to evaluate the models, as in Flament (2019), we compute the
accuracy Acc
We compare five different reconstructions between 200 and 900 Ma to
assess the consequences of alternative assumptions and approaches for
reference frame construction (Fig. 3), including a standard paleomagnetic
reference frame (Merdith et al., 2021) (PMAG), a no-net-rotation
reference frame (NNR), our reference frame which is optimized with respect
to tectonic rules (OPT), an orthoversion reference frame from Cao et al. (2021a) following Mitchell et al. (2012) (ORTHO), and a reference frame
based on a combination of paleomagnetic and geological data incorporating the
alignment of plume products at the surface with fixed LLSVP edges
(Torsvik and Cocks, 2019) (FIX_LLSVP). At 200 Ma (Fig. 3a)
all reconstructions are quite similar; however, by 300 Ma a visible
difference emerges between FIX_LLSVP and all other
reconstructions in terms of the longitudinal positions of continents. At
this time, South America is located about 20
For times older than 500 Ma (Fig. 3b) we only compare four reconstructions as the model by Torsvik and Cocks (2019) does not reach back to 600 Ma. Firstly, there is distinctive similarity between the OPT and NNR reconstructions, even though the OPT case minimizes trench migration speeds and penalizes global continental velocities in addition to minimizing net rotation. The primary reason for this is that trench migration and net rotation are relatively closely coupled, so minimizing one also reduces the other to a large extent, and continents typically do not tend to move fast when both net rotation and trench migration are minimized, even if explicit constraints are not introduced for continents. This comparison provides an important insight, namely that the simple lithospheric no-net-rotation rule used to produce the NNR model produces results that are not dramatically different from a model optimized by a set of more general tectonic rules. This is important because NNR models have been frequently used in tectonic and mantle flow models for practical reasons (e.g. Mao and Zhong, 2021; Zhong and Rudolph, 2015; Behn et al., 2004; Kreemer and Holt, 2001) in the absence of other available mantle reference frames. Our results here suggest that NNR reference frames are not entirely unrealistic from a tectonic rules point of view. In terms of the relative importance of plate motion optimization parameters, our results suggest that minimizing net rotation is the most important one, with minimizing subduction zone migration of secondary importance, as minimizing net rotation also reduces subduction zone migration to some extent (also see Müller et al., 2019, for a discussion of the effect of changing the relative weight of these parameters). Preventing the speed of continents from exceeding continental speed limits is the least important parameter. We introduced it to ensure that large swathes of synthetically reconstructed ocean floor would not result in a minimal net rotation solution that imposes unreasonable motions on the smaller continental regions.
The PMAG model is expectedly quite different, with no longitudinal and plate
speed constraints imposed, while the orthoversion model (ORTHO) is very
different by design, as it follows the idea that Rodinia formed
about 90
Plate reconstructions based on alternative approaches for modelling absolute plate motions, with reference frames based on paleomagnetic data (PMAG) (Merdith et al., 2021), no-net-rotation (NNR), tectonic-rules-based optimization (OPT), orthoversion from Cao et al. (2021a) following Mitchell et al. (2012), and a combination of paleomagnetic data and aligning LIPs with the edges of LLSVPs assumed to be stationary (Torsvik and Cocks, 2019), covering the time period from 200–900 Ma. The reconstruction of Torsvik and Cocks (2019) does not extend back to 600 Ma and older. Continents are outlined in beige, while subduction zones are toothed black lines. The present-day position of continents is shown in light grey in the background as a reference.
The dramatic reduction of lithospheric net rotation in our optimized
reference frame relative to the PMAG reference frame is illustrated in
Fig. 4a, which compares net rotation of our optimized model with the
paleomagnetic reference frame from Merdith et al. (2021) and the mantle
reference frame model by Matthews et al. (2016) incorporating the
Paleozoic reconstruction from Domeier and Torsvik (2014), with the latter
being similar to the model of Torsvik and Cocks (2019) shown in Fig. 3.
These two Paleozoic models (Domeier and Torsvik, 2014; Torsvik and Cocks,
2019) are constructed as mantle reference frames by following the idea that
by applying a TPW correction and aligning LIPs and kimberlites with the
edges of LLSVPs an approximation of the “true” latitude and longitude of
plates relative to the mantle is obtained. If this were the case, we would
expect to see the large fluctuations in lithospheric net rotation seen in a
model based on paleomagnetic data alone (Fig. 4b) dramatically reduced.
However, the result of applying empirical TPW and longitudinal corrections
as proposed by Domeier and Torsvik (2014) results in 0.4–1.5
Compared to the paleomagnetic model (Fig. 5a), our optimized model (Fig. 5b)
exhibits significantly reduced trench-orthogonal subduction zone migration
scatter as well as reduced median absolute deviation of trench motion (Fig. 6), reflecting the suppression of fast, geodynamically unreasonable global
trench migration rates. The substantial overall improvement in the scatter
of trench migration velocities is expressed in limiting the bulk of trench
advance to a relatively narrow band of rates to 0–3 cm yr
The opposite holds for times of supercontinental dispersal, during which the
ring of subduction zones surrounding a supercontinent rolls back oceanward,
accommodating the creation of new internal ocean basins. The spread of
trench migration during the dispersal of Rodinia (
Histogram of the trench-orthogonal overriding plate speed for
Median trench motion speed with median absolute deviation error range for the unoptimized plate motion model in red and the optimized model in blue using a 5 Myr moving average window. Periods of supercontinent stability are characterized by very slowly moving subduction zones, but Rodinia dispersal and the following long period of the successive opening and closing of a number of internal ocean basins resulted in a larger prevalence of relatively fast subduction zone migration compared with Pangea dispersal. See text for discussion.
The third parameter we use to impose tectonic rules on our optimized plate
motion model is global continental rms speeds. The paleomagnetic reference
model (Fig. 7a) is characterized by plate and continental speeds that are
frequently 50 % or more above those of the optimized model (Fig. 7b),
which limits maximum continental rms speeds below the continental
“speed limit” of 10 cm yr
Root mean square (rms) speeds of all plates and continents in the
paleomagnetic model
Our mantle flow models are driven by imposed surface plate velocities, subduction zone locations and geometries (Supplement Animation S1), and reconstructed age-area distributions of the ocean crust through time (Figs. 8, 9, Supplement Animation S2), following the method of Williams et al. (2021). The predicted evolution of mantle temperature primarily records the effect of changing subduction zone topologies and convergence velocities as well as the age of subducting slabs through time. Here we focus on the evolution of basal mantle structure (Figs. 10 and 11), which is particularly relevant for understanding the history of deep mantle plumes, and on the upper mantle structure through time, which is connected to surface magmatism via upper mantle temperature anomalies and upwellings. To do this, we compare output from two mantle flow models, OPT1 (Fig. 10a) and OPT2 (Fig. 10b), which differ in buoyancy ratio for the basal mantle layer (Table 1) (see also Supplement S3–S10). Model outputs for the NNR and PMAG models are included in the Supplement (Figs. S1–S4, S6, and S7).
Reconstruction at 1 Ga with the synthetic age of the ocean floor reconstructed using the method by Williams et al. (2021). Mid-ocean ridges are shown as white lines, subduction zones as toothed black lines, and regions of continental crust filled with grey; individual continental blocks are labelled. Afg: Afghanistan, KMT: Kyrgyz Middle Tianshan, SC: southern China, NC: northern China, WAC: West Africa Craton.
During the first 400 million years of model evolution (1000–600 Ma) the
basal mantle structure is dissected into a network of ridges as a response
to a widely dispersed network of subduction zones from 1000–760 Ma,
preventing any extensive basal mantle structure akin to present-day LLSVPs
from forming (Fig. 10a). Between 760 and 560 Ma, an equatorially centred
subduction girdle forms in our model, restricted to a latitude range less
than 60
Oceanic crustal age grids from 1 Ga to the present constructed from plate rotations and boundaries in 100 Myr intervals following Williams et al. (2021), with plate boundaries and continents coloured as in Fig. 8.
These results are consistent with the inference from Cao et al. (2021a)
that it may take 160–240 Myr for the basal mantle structure to reflect
changes in subduction zone geometry at the surface. Our model thus records
five distinct intervals of mantle convection geometry: (1) a network of
dissected basal ridges (1000–600 Ma), (2) a short-lived degree-2 basal
mantle structure with upwellings centred on the North and South Pole
(600–500 Ma), (3) a transitional state in which the north polar basal
structure migrates southward and gradually evolves into a Pacific-centred
structure while the south polar structure is dissected by subducting slabs
and disintegrates into a network of ridges (500–400 Ma), (4) a
Pacific-centred degree-1 structure (400–200 Ma), and (5) a degree-2 structure
akin to what is observed today (160–0 Ma), which is composed of a long-lived
Pacific basal structure joined by an African counterpart that gradually
amalgamates during a
Map view of mantle temperature anomalies relative to the mean
temperature at 2677 km depth for our geodynamic reference model OPT1
Global equatorial mantle cross-sections for our geodynamic
reference model OPT1
Upper mantle temperature anomaly maps at
Map view of mantle temperature anomalies relative to the mean temperature at 396 km depth for our geodynamic reference model OPT1 in 100 Myr increments since 800 Ma. Reconstructed present-day coastlines and continental sutures are shown as thin grey lines, while outlines of continents are displayed as bold grey lines. Subduction zones are bold magenta lines with triangles pointing towards overriding plates, while mid-ocean ridges are shown as yellow lines.
We use virtual transparent globes displaying the modelled time-dependent
mantle temperature structure to visualize the response of the 3D geometry of
the basal layer and associated upwellings to the evolving geometry and
volume of slabs descending in the mantle (Fig. 14). The development of basal
mantle structures in response to subduction in our model is illustrated in
two views of the mantle through time: one view is centred at
270
Visualization of modelled mantle structure through time focussing
on the Pacific hemisphere since 800 Ma in 100 Myr intervals with central
meridians at 270
As noted in previous work (Torsvik et al., 2010), the volcanic eruptions
reconstructed at their time of eruption and shown at present day are
generally close to LLSVPs, although this depends on the reconstruction that
is used (Fig. 15). Reconstructed locations of volcanic eruptions are also
close to mobile BMSs predicted by mantle flow models (Fig. 16) (Flament
et al., 2022). The statistical significance of the median distance between
volcanic eruptions and BMSs (see Fig. 17), expressed as a fraction
For cases OPT2, PMAG, and NNR,
High-velocity (white) and low-velocity (grey) regions revealed by
Low-temperature (white) and high-temperature (grey) regions predicted by plate–mantle models OPT2, PMAG, NNR, and OPT1 as indicated in 100 Myr increments from 900 Ma, as well as the location of volcanic eruptions (magenta squares, EY17, Ernst and Youbi, 2017, and green diamonds, J18, Johansson et al., 2018) and kimberlites (black circles, Tappe et al., 2018) reconstructed at the age of interest, shown for eruptions that occurred within 10 Myr of the age of interest. The black lines indicate a value of 5 (solid) and a value of 1 (dotted) in a vote map for low-velocity regions in S-wave tomographic models (Lekic et al., 2012).
Sample empirical distribution functions (EDFs; blue lines)
showing the cumulative probability of minimum angular distances between 1168
volcanic eruptions and the nearest basal mantle structure over the last 960 Myr for two tomographic models and two mantle flow models. Grey lines are a
series of 1000 EDFs showing the same quantity for points randomly
distributed around the globe.
Match between predicted model basal mantle structures, volcanic
eruption locations, and tomographic models.
We use our optimized absolute plate motion model as a reference for the
time-averaged median distance
We did not attempt to identify a model that falls within range of
tomographic models for
The spatial match between modelled lower mantle temperature clusters between 1000 and 2800 km depth at present day from models OPT1 and OPT2 versus seismic tomographic clusters from tomographic models GyPSuM-S, HMSL-S, S40RTS, S362ANI, Savani, SAW24b16, and SEMUCB-WM1d (Auer et al., 2014; French and Romanowicz, 2014; Houser et al., 2008; Kustowski et al., 2008; Mégnin and Romanowicz, 2000; Ritsema et al., 2011; Simmons et al., 2010) is illustrated in Fig. 13. The relatively larger basal mantle structure buoyancy ratio in model OPT2 relative to our reference model OPT1 results in a larger lateral extent of lower mantle structures (Fig. 12a, b). In particular, the anomalously hot lower mantle cluster centred on the Pacific extends significantly beyond the anomalously slow structures captured in the tomography models (Fig. 13b), while the anomalously hot structure underneath Africa is also more extensive in OPT2 than in OPT1. In this instance, the spatial extent of this structure as imaged in the tomography models is somewhat underestimated in OPT1 (Fig. 19a), highlighting the difficulty of finding a model that matches equally well in all regions.
The model accuracy, i.e. the fraction of correct predictions of all our
mantle flow models in terms of the clusters analysed here, is best
compared to tomographic models Savani (Auer et al., 2014) and HMSL-S
(Houser et al., 2008) at
In contrast to the model accuracy, sensitivity is the true positive rate at which the mantle flow model reproduces the geographical distribution of slow clusters in tomographic models; i.e. it represents the percentage of anomalously slow mantle from tomographic models that is correctly matched by modelled hot mantle temperature anomalies (Fig. 20b). Model sensitivity covers a range of 52 %–65 %, clearly differentiating our preferred model OPT1 from all other models (Fig. 19b). The OPT1 sensitivity is larger than 61 % for all tomographic models with the exception of S362ANI (Kustowski et al., 2008) and SAW24B16 (Mégnin and Romanowicz, 2000). In terms of sensitivity, the paleomagnetic and no-net-rotation mantle flow models are the lowest-ranked models with a mean of 56 %–57 % averaged across all seven tomographic models. The top three tomographic models in terms of their match to mantle flow model OPT1 are SEMUCB-WM1 (French and Romanowicz, 2014), Savani (Auer et al., 2014), and S40RTS (Ritsema et al., 2011), with a sensitivity between 64 % and 66 %. In summary, our preferred mantle flow model OPT1 produces the highest mean for accuracy (72 %) and sensitivity (61 %) averaged across all seven tomographic models, while Savani (Auer et al., 2014) and S40RTS (Ritsema et al., 2011) consistently produce high scores for models OPT1 and OPT2 for both accuracy and sensitivity (Fig. 20a, b).
Spatial match between modelled lower mantle temperature clusters
between 1000 and 2800 km depth at present day from models OPT1
Quantitative match between predicted lower mantle temperature
clusters between 1000 and 2800 km depth of our four mantle flow models
OPT1, OPT2, PMAG, and NNR at present day and seven seismic tomographic
clusters from models GyPSuM-S, HMSL-S, S40RTS, S362ANI, Savani, SAW24b16, and
SEMUCB-WM1 shown as model accuracy
Our tectonic-rules-based absolute plate motion model in a mantle reference
frame provides an alternative methodology to constrain both latitudes and
longitudes of plates and continents through time. Our optimized model lacks
the distinct northward migration of Pangea during and after its assembly
featured in the model by Merdith et al. (2021) (compare reconstructions
at 400 and 300 Ma in Fig. 3a). This 60
In terms of subduction zone migration, our results suggest that the
distribution of trench migration, largely confined to a relatively narrow
range of
After the assembly of Gondwana a number of new ocean basins formed around its periphery, separating it from Laurentia, Baltica, Siberia, and other blocks now part of Asia, successively creating and destroying ocean basins including the Iapetus Ocean (Fig. 8). The period was characterized by numerous relatively short subduction zones, which have the capacity to roll back faster than long subduction zones (Schellart et al., 2008). After 490 Ma the ephemeral Iapetus Ocean was replaced by the Rheic Ocean, separating several arc terranes from northern Gondwana, also characterized by fast trench migration of relatively short subduction zones. Ultimately the difference in the spread of trench migration behaviour (shown as its median absolute deviation in Fig. 6) between the Paleozoic zippy tricentenary compared to the relatively sluggish late Mesozoic–Cenozoic dispersal of Pangea reflects the fact that the latter was characterized by a smaller number of relatively long subduction zones which cannot roll back easily, as shown by mantle flow models (Schellart et al., 2007). The rollback potential of subduction zones wider than 4000 km is limited by the lacking ability of their central portions to migrate (Schellart et al., 2007). In contrast, much of the Paleozoic Era was characterized by a profusion of relatively short subduction zones in the Merdith et al. (2021) reconstructions, many associated with rapidly evolving internal ocean basins (Fig. 6b).
The most surprising outcome of our mantle reference frame optimization using
a set of tectonic rules is that the resulting absolute plate rotations
produce an orthoversion model in which the centres of Rodinia and Pangea are
approximately offset from each other by 90
In our model Rodinia is located father south (mostly south of 60
Similarly to previous models, our mantle flow model shows that the geometry
and location of basal mantle structures are controlled by subducting slabs
(e.g. Bunge et al., 1998; Garnero and Mcnamara, 2008; Zhong and Rudolph,
2015; Bull et al., 2014; King, 2015). Zhong et al. (2007) proposed that
the evolution of subduction across supercontinent cycles may cause
alternations between degree-1 and degree-2 planform convection. In contrast,
Cao et al. (2021a), using simplified plate motion models to test
alternative absolute reference frames since 1 Ga including an orthoversion
and no-net-rotation model, could not find evidence of degree-1 mantle
convection forming in their models. Our mantle flow model, which differs
from that used in Cao et al. (2021a) in that we use the plate motion
model by Merdith et al. (2021) and a novel mantle reference frame, does
demonstrate the development of a degree-1 planform, but as a relatively rare
occurrence over the last 1 Gyr (Fig. 10a). In our model, a Pacific-centred
degree-1 basal structure forms in the lead-up to the assembly of Pangea
around 400 Ma (Figs. 10, 11) underneath a long-lasting superocean, with the
underlying mantle largely protected from descending slabs after
The major changes in subduction geometry over the last 1 Gyr therefore dictate that basal mantle structures are ephemeral and constantly changing in response to subducting slabs pushing against their edges or flowing over them (Fig. 14). Akin to the extremely heterogenous lower mantle structures seen in the seismic tomography images (e.g. Schuberth et al., 2009; Tkalčić et al., 2015) our model produces bundles of basal mantle upwellings very similar to the thermochemical upwellings enriched in denser than average material interpreted by Davaille and Romanowicz (2020) based on a combination of seismic tomography and fluid mechanic constraints (Fig. 14). In our mantle flow model basal mantle structures are always composed of a network of upwelling structures, from which mantle plumes emanate. These networks may form and evolve without “LLSVP-like” extensive mantle upwellings, as is the case in our model from 1000–600 Ma, a period without either degree-1 or degree-2 lower mantle structures (Fig. 14, Supplement Animation S11). Their absence during this period reflects the widely distributed, rapidly evolving network of subduction zones, preventing large coherent basal mantle structures from forming (Figs. 10, 14). Large basal structures form from the coalescence of distributed ridges as they are being pushed towards each other by descending slabs in nearby regions (Fig. 14, Supplement Animation S11) (see also Bower et al., 2013; Davies et al., 2012).
Most slabs descend into the lower mantle, but we find that slab stagnation occurs both in the transition zone and in the middle to lower mantle around 1000–1400 km depth, as is observed in tomographic models (Shephard et al., 2017). However, we point out here that our model does not include phase transitions. The likelihood of stagnation at either depth appears to be increased by fast trench retreat or advance and/or subduction of relatively young lithosphere. Accumulations of slabs below the middle to lower mantle are often detached from shallower slabs and move laterally (Figs. 10, 14, Supplement Animation S11). Therefore, it cannot be expected that slab accumulations imaged in seismic tomography at depths far below 1400 km can be used as reliable markers for past locations of subduction zones, as implied in the subduction reference frame by Van Der Meer et al. (2010). Our mantle flow model further illustrates the effects of dynamic slab thickening and buckling (Lee and King, 2011) as slabs move from the transition zone into the lower mantle, and slabs also break off (Gerya et al., 2004; von Blanckenburg and Davies, 1995) when subduction ceases, due to rapid trench advance or retreat, or due to a change in the sign of trench motion (e.g. from advance to retreat). When slabs reach the lowermost mantle, they move laterally towards upwelling regions, pushing hot, low-viscosity basal structures to form steep ridges along their margins (Supplement Animations S3, S4, S11). The coalescence of ridge-like upwellings that are being pushed towards each other by slabs results in enlarged structures with internal and marginal ridges (Fig. 14, Supplement Animation S11). Slabs that have sunk to the lowermost mantle gradually heat up and occasionally rise and spread over the edge of basal mantle upwellings, and mantle plumes form along basal ridges either in the interior or along the edges of basal mantle structures (Fig. 14, Supplement Animation S11). The roots of individual plumes are not stationary but migrate in response to the deformation of basal structures, as found previously (e.g. Cao et al., 2021b; Hassan et al., 2016; Arnould et al., 2019). Plume tilt mostly forms in response to relatively fast plate motion and induced sub-horizontal lower mantle flow (Fig. 14, Supplement Animation S11).
The spatial match between lower mantle temperature clusters of our preferred model OPT1 with tomographically imaged lower mantle structure (Fig. 19a) demonstrates that our model reproduces the observed large-scale mantle structure quite well. It is noteworthy that the unoptimized model PMAG, not representing a mantle reference frame, reaches an equivalent accuracy as the optimized models OPT1 and OPT2 (Fig. 20a). This reflects the fact that the present-day mantle structure is largely the result of the post-250 Ma subduction history (Flament, 2019) and that the unoptimized versus the optimized models do not show any dramatic differences in the position of plates and subduction zones during this time (compare reconstructions of the two models at 300 and 200 Ma in Fig. 3a). The post-250 Ma differences in the subduction history between these models are not large enough to create any major dissimilarities between the modelled lower mantle structure at present day. Stark differences between these plate models are confined to pre-300 Ma times (Fig. 3). The slightly larger excess density of the basal mantle layer in model OPT2 compared to OPT1 (Table 1) results in spatially more extensive basal mantle upwellings in OPT2 relative to OPT1 (Figs. 11a, b, 14a, b). This slightly improves the match to most seismic tomographic models in the African hemisphere in OPT2, while worsening the match in the Pacific hemisphere (Fig. 19b). In other words, in OPT2, the Pacific LLSVP is somewhat too extensive compared with tomographic images, while in OPT1 the African LLSVP is not sufficiently extensive, as reflected in the variation of the size of the areas labelled as true positive (Fig. 19a, b). This may reflect the fact that the excess density of the Pacific versus African LLSVPs is not identical. This is confirmed by a recent analysis of global shear-wave tomography models, suggesting that the African LLSVP has a relatively lower density and is less stable than its Pacific counterpart (Yuan and Li, 2022).
Upper mantle temperature anomalies through time at
Extensive anomalously cool regions in the upper mantle occur in our model under Siberia, Baltica, and North America (420–380 Ma, early to middle Devonian), North America (100–40 Ma, Late Cretaceous to early Cenozoic), and along eastern–southern Asia and Zealandia (after 100 Ma) (Fig. 14). Devonian magmatism, including intraplate magmatism, in Siberia, Baltica, and North America was recently summarized by Ernst et al. (2020). Non-plume-related intraplate magmatism across this region may have been driven by subducted volatiles accumulating in the mantle transition zone under these continental regions and driving the formation of volatile-bearing transition zone plumes which have been related to both ocean island basalt-type mafic and felsic melts (Safonova et al., 2015). Post-100 Ma subduction-related intraplate volcanism (including kimberlites) far inland from active trenches has been described for North America (Currie and Beaumont, 2011; Heaman et al., 2003), eastern Asia (Cao et al., 2021c; Wu et al., 2005), and Zealandia (Mather et al., 2020; Mortimer and Scott, 2020).
The primary differences between our optimized plate–mantle models OPT1 and
OPT2 compared to the PMAG plate–mantle model are driven by the much
larger net rotation implicit in the PMAG model and the difference in the
reconstructed paleo-latitude of Rodinia, which is centred on low latitudes in
the PMAG model versus a high southern latitude in the optimized plate model
(Fig. 3b). This difference illustrates that our model implies a substantial
degree of TPW due to the difference between the OPT and PMAG configurations.
Using the PMAG plate model as a surface condition for a mantle convection
model is inherently unreasonable, as the large net rotation embedded in the
model, reaching peaks of over 1.2
The differences in the modelled history of basal mantle structures, i.e. their location, size, and heterogeneity, have implications for modelling the Earth's magnetic field through time. LLSVPs increase the insulation of the core–mantle boundary, decrease the temperature gradient, and suppress core–mantle boundary heat flow (Li et al., 2018). Glatzmaier et al. (1999) suggested that the polar core–mantle boundary heat flow may be key to driving magnetic reversal frequency. In contrast, Olson et al. (2010) found that the average polarity reversal frequency is sensitive to the total core–mantle boundary heat flow and to the total heat flow at the Equator, while reversal frequency may also increase with the amplitude of the boundary heterogeneity. Our basal mantle structure models could be used to evaluate the effect of alternative plate–mantle models on the spatio-temporal patterns of core–mantle boundary heat flow and magnetic reversal frequency. Such models could also be used to test the validity of alternative reference frames in terms of how well modelled magnetic reversal frequencies match observed ones.
Further future tests of our absolute reference frames in terms of their suitability as mantle reference frames may include dynamic surface topography models derived from plate–mantle models. Such models could be compared against geologically mapped continental flooding patterns, following approaches designed to separate effects of eustasy and dynamic topography on continental flooding (e.g. Cao et al., 2019; Müller et al., 2018). In terms of testing alternative orthoversion models, if continents move eastwards after Rodinia breakup, as in our optimized mantle reference frame, one would expect the eastern portions of continents to be flooded first as they move towards dynamic topography lows associated with subduction zones to the east of Rodinia. In contrast, if continents move westwards after Rodinia breakup as suggested by Mitchell et al. (2012) and implemented as a model with evolving plate boundaries by Cao et al. (2021a), one would expect to see the western portions of continents inundated first after Rodinia breakup.
We have used “tectonic rules” to optimize an absolute mantle reference frame
devoid of unreasonably large lithospheric net rotation, excessive subduction
zone migration rates, and excessive speeds for plates hosting large
continents. Our model results in net rotation consistently below
0.25
Our mantle flow model is driven by the imposed plate motions and subduction
history and results in a succession of deep mantle states without or with
large basal mantle structures akin to present-day LLSVPs. Our numerically
modelled basal mantle structures bear a striking resemblance to the mantle
tomographic images by Davaille and Romanowicz (2020). Their tomographic
model, together with laboratory experiments, led to the view that LLSVPs are
composed of bundles of thermochemical upwellings, whose shape is controlled
by subduction history, resulting in a position and geometry of LLSVPs that
are time-dependent (Davaille and Romanowicz, 2020). This view is
supported by our work, which explicitly links the evolution of the plates
and plate boundaries over time with mantle structure evolution. Our model
records five distinct intervals of mantle convection evolution over the last
1000 Myr. Initially, a broad network of basal ridges forms between 1000
and 600 Ma, followed by the formation of a short-lived degree-2 basal mantle
structure centred on the North and South Pole between 600 and 500 Ma. It
is superseded by a transitional phase during which the north polar basal
structure migrates southward and gradually morphs into an extensive
Pacific-centred basal structure, while the south polar structure is dissected
by subducting slabs and disintegrates into a network of ridges between
500 and 400 Ma. Subsequently, a Pacific-centred degree-1 structure forms and is
stable between 400 and 200 Ma, which is superseded by a basal degree-2
mantle structure after
The codes used for this paper are available on the public EarthByte and
GPlates GitHub sites. This includes absolute plate motion model optimization
code at
The optimized plate model, including paleo-oceanic crustal age grids, used
in this paper is available on the EarthByte webdav site at
The data and video supplements are available on Zenodo at
The supplement related to this article is available online at:
RDM conceived and coordinated the research underpinning the paper and wrote the paper. JC contributed to the design of the absolute plate model optimization code, executed the optimization runs, and contributed to the paper. MT wrote the original optimization code and contributed to the paper. SEW contributed to the plate model optimization code, wrote Jupyter notebooks to visualize results, and contributed to the paper. XC executed the mantle flow models and contributed to the analysis of the results and to the paper. NF oversaw the design of the mantle flow models and contributed to the model analysis and to the paper. OFB visualized the mantle flow models. SZ and AM contributed to the plate model and the paper.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This research was supported by the Australian Research Council under grants LP210100173, LP170100863, and DE210100084 and supported by the Australian Government's National Collaborative Research Infrastructure Strategy (NCRIS), with access to computational resources provided by the National Computational Infrastructure (NCI) through the National Computational Merit Allocation Scheme and through the Sydney Informatics Hub HPC Allocation Scheme, which is supported by the Deputy Vice-Chancellor (Research), University of Sydney, and ARC grant LE190100021.
This research has been supported by the Australian Research Council (grant nos. LP210100173, LP170100863, DE210100084, and LE190100021).
This paper was edited by Susanne Buiter and reviewed by D. Rhodri Davies and Scott King.