DOI: 10.5281/zenodo.15233548
title: Muller2025 Mantle Reference Frame Plate Model based on Cao et al. (2024)

description: This plate model has been placed in a mantle reference frame, based on the plate model by Cao et al. (2024). Relative plate motions are identical, and plate topologies are close to identical, with the exception of a small number of subduction zones that were moved slightly further away from continental outlines to comply with the method described in Müller et al. (2022) to reconstruct the extended outlines of continents in deep time. The model is equivalent to the "Shirmard2025" model.

The mantle reference frame was derived using the optimisation approach as described in Müller et al. (2022). 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. We use continental Africa as the reference. 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). We also compute a fourth constraining criterion: (4) median global continental absolute plate velocity (PV). We introduce continental absolute plate velocities as 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 the reconstructed ocean floor that is now subducted, based on a variety of indirect pieces of geological evidence (Merdith et al., 2021). The constraining criteria are applied to the absolute plate motion model optimization with the following assumptions/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 plate motion model and present-day hotspot chains is minimized, and (4) global continental median plate speed remains < 60 mm/yr. The contribution of individual optimization parameters to the overall inversion are initially scaled by relative magnitude and then weighted by empirically determined weights. For times older than 80 Ma, NR=1, TM=0.5, PV=0.5, HS=0 (0-80 Ma, NR=TM=PV=HS=1).

To estimate the original boundaries of preserved outlines of continents reconstructed to their past positions given a rotation model we applied a continent contouring algorithm to create continental outlines, using the code in this github repository: https://github.com/EarthByte/continent-contouring. The algorithm is based on marching squares, a 2D adaptation of the Marching Cubes algorithm applied to the surface of a sphere. The continental outlines are expanded by a time-dependent user-specified buffer distance (see github repo for details).

The optimized rotation files are:optimisation/1000_0_rotfile_20240725.rotoptimisation/1800_1000_rotfile_20240725.rot The GPlates project "1.8_Ga_reconstruction_mantle_ref_frame.gproj" can be used (using the GPlates software) to compare the optimized with the original ref frame. There are two optimized rotation layers (yellow) in the project. They provide the same reference frame, but organised differently. The first layer contains a single combined rotation file this is basically the original two rotation files combined into one but with the addition of the optimised rotations, expressed as 005-000 in terms of plate IDs. The second contains the above-mentioned two rotation files but with the 005-000 optimised frame merged into them. The latter is recommended for end users, and is used when reading this rotation model with the GPlately plate model manager. In this representatiuon of the rotations we remove plate 005 (the optimized frame) to avoid confusing end users, who can use 000 as anchor plate as is usually the case for absolute reference franmes in GPlates plate models. 

However, the former model (retaining the reference to the 005-000 reference frame) can be useful for power users, if they want to keep track of the original relative rotations and also those who may want to analyse the difference rotations between the original paleomagnetic reference frame and the optimised mantle reference frame rotations (i.e. 005-000). If the user loads the GPlates project containing the optimised model, and then loads the rotation file starting with "optimised_rotation_model_" in the "optimisation/" sub-directory (which creates a new yellow rotation layer in GPlates), and setting the anchor plate ID to 005, then this will reflect the unoptimized (original) pmag-based rotation model, ie, setting 005 as anchor plate ID removes the optimised rotations. 

What has changed in this revision:

- Removed unnecessary repeats in segments in TopologicalClosedPlateBoundaries- Adjusted segment sequence in TopologicalClosedPlateBoundaries to resolve gaps and overlaps- Removed erroneously duplicated TopologicalClosedPlateBoundaries- Ensured neighbouring TopologicalClosedPlateBoundaries used the same feature segment along their boundaries- Spatially extended feature segments to close TopologicalClosedPlateBoundaries that had drifted open- Restore unresolved feature references in TopologicalClosedPlateBoundaries- Insert new feature references in TopologicalClosedPlateBoundaries to deliniate where connections should be to maintain - consistancy between neighbouring TopologicalClosedPlateBoundaries

Time periods for changes:

- Very few 1800-801 Ma- Mostly scattered 800-0 Ma





The seafloor age and spreading rate grids associated with this model can be found at https://repo.gplates.org/webdav/PlateModel_Age_SR_Grids/Muller_etal_2025/ .