Tidal Evolution of Close Binary Asteroid Systems

We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less than five times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function, based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system, e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate, semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent.Comment: 40 pages, 2 tables, 8 figure

A review of analogue modelling of geodynamic processes: Approaches, scaling, materials and quantification, with an application to subduction experiments

We present a review of the analogue modelling method, which has been used for 200 years, and continues to be used, to investigate geological phenomena and geodynamic processes. We particularly focus on the following four components: (1) the different fundamental modelling approaches that exist in analogue modelling; (2) the scaling theory and scaling of topography; (3) the different materials and rheologies that are used to simulate the complex behaviour of rocks; and (4) a range of recording techniques that are used for qualitative and quantitative analyses and interpretations of analogue models. Furthermore, we apply these four components to laboratory-based subduction models and describe some of the issues at hand with modelling such systems. Over the last 200 years, a wide variety of analogue materials have been used with different rheologies, including viscous materials (e.g. syrups, silicones, water), brittle materials (e.g. granular materials such as sand, microspheres and sugar), plastic materials (e.g. plasticine), visco-plastic materials (e.g. paraffin, waxes, petrolatum) and visco-elasto-plastic materials (e.g. hydrocarbon compounds and gelatins). These materials have been used in many different set-ups to study processes from the microscale, such as porphyroclast rotation, to the mantle scale, such as subduction and mantle convection. Despite the wide variety of modelling materials and great diversity in model set-ups and processes investigated, all laboratory experiments can be classified into one of three different categories based on three fundamental modelling approaches that have been used in analogue modelling: (1) The external approach, (2) the combined (external + internal) approach, and (3) the internal approach. In the external approach and combined approach, energy is added to the experimental system through the external application of a velocity, temperature gradient or a material influx (or a combination thereof), and so the system is open. In the external approach, all deformation in the system is driven by the externally imposed condition, while in the combined approach, part of the deformation is driven by buoyancy forces internal to the system. In the internal approach, all deformation is driven by buoyancy forces internal to the system and so the system is closed and no energy is added during an experimental run. In the combined approach, the externally imposed force or added energy is generally not quantified nor compared to the internal buoyancy force or potential energy of the system, and so it is not known if these experiments are properly scaled with respect to nature. The scaling theory requires that analogue models are geometrically, kinematically and dynamically similar to the natural prototype. Direct scaling of topography in laboratory models indicates that it is often significantly exaggerated. This can be ascribed to (1) The lack of isostatic compensation, which causes topography to be too high. (2) The lack of erosion, which causes topography to be too high. (3) The incorrect scaling of topography when density contrasts are scaled (rather than densities); In isostatically supported models, scaling of density contrasts requires an adjustment of the scaled topography by applying a topographic correction factor. (4) The incorrect scaling of externally imposed boundary conditions in isostatically supported experiments using the combined approach; When externally imposed forces are too high, this creates topography that is too high. Other processes that also affect surface topography in laboratory models but not in nature (or only in a negligible way) include surface tension (for models using fluids) and shear zone dilatation (for models using granular material), but these will generally only affect the model surface topography on relatively short horizontal length scales of the order of several mm across material boundaries and shear zones, respectively

Introduction to the special issue celebrating 200 years of geodynamic modelling

Since the first published laboratory models from Sir James Hall in 1815, analogue and numerical geodynamic modelling have become widely used as they provide qualitative and quantitative insights into a broad range of geological processes. To celebrate the 200th anniversary of geodynamic modelling, this special issue gathers review works and recent studies on analogue and numerical modelling of tectonic and geodynamic processes, as an opportunity to present some of the milestones and recent breakthroughs in this field, to discuss potential issues and to highlight possible future developments

Control of slab width on subduction-induced upper mantle flow and associated upwellings: Insights from analog models

The impact of slab width W (i.e., trench-parallel extent) on subduction-induced upper mantle flow remains uncertain. We present a series of free subduction analog models where W was systematically varied to upscaled values of 250–3600 km to investigate its effect on subducting plate kinematics and upper mantle return flow around the lateral slab edges. We particularly focused on the upwelling component of mantle flow, which might promote decompression melting and could thereby produce intraplate volcanism. The models show that W has a strong control on trench curvature and on the trench retreat, subducting plate, and subduction velocities, generally in good agreement with previous modeling studies. Upper mantle flow velocity maps produced by means of a stereoscopic particle image velocimetry technique indicate that the magnitude of the subduction-induced mantle flow around the lateral slab edges correlates positively with the product of W and trench retreat velocity. For all models an important upwelling component is always produced close to the lateral slab edges, with higher magnitudes for wider slabs. The trench-parallel lateral extent of this upwelling component is the same irrespective of W, but its maximum magnitude gets located closer to the subducting plate in the trench-normal direction and it is more focused when W increases. For W ≤ 2000 km the upwelling occurs laterally (in the trench-parallel direction) next to the subslab domain and the mantle wedge domain, while for W ≥ 2000 km it is located only next to the subslab domain and focuses closer to the trench tip, because of stronger poloidal flow in the mantle wedge extending laterally

Mantle constraints on the plate tectonic evolution of the Tonga-Kermadec-Hikurangi subduction zone and the South Fiji Basin region

The Tonga–Kermadec–Hikurangi subduction zone is a major plate boundary in the Southwest Pacific region, where the Pacific plate subducts westward underneath the Australian plate. Considerable controversy exists regarding the Cenozoic evolution of this subduction zone, its connection with the Vitiaz–Solomon trench, the opening of adjacent backarc basins (South Fiji Basin, Norfolk Basin), and the obduction of ophiolites in New Caledonia and New Zealand. We analyse three tectonic reconstructions from 45 Ma to the present that represent three end-member tectonic scenarios. The first model involves an approximately west-dipping Tonga–Kermadec–Hikurangi subduction zone that rolls back clockwise, and an approximately east-dipping New Caledonia–Northland subduction zone that rolls back anticlockwise until ca 21 Ma. The other models involve only the Tonga–Kermadec–Hikurangi subduction zone that rolls back clockwise in one, and anticlockwise in the other model. We tied the three reconstructions to an Indo-Atlantic moving hotspot reference frame, indicating how the subduction zones migrated with respect to the lower mantle at 45–0 Ma, thereby predicting the location of slab material in the mantle. The predicted slab locations have been compared with a global P-wave tomography model (UU-P07) that gives insight into mantle structure and fossil slab locations. Minor agreement is achieved for the anticlockwise model, which fails to predict most of the lower mantle Tonga–Kermadec–Hikurangi slab anomaly below the South Fiji Basin and North Fiji Basin. Moderate agreement is achieved for the clockwise model, which predicts most of the lower mantle Tonga–Kermadec–Hikurangi slab anomaly below the South Fiji Basin, but not its northernmost extent below the North Fiji Basin. The model involving two oppositely dipping subduction zones shows good agreement, predicting slab anomalies at the right depth and geographical location for the Tonga– Kermadec–Hikurangi and Solomon–Vitiaz subduction segments, as well as for the New Caledonia– Northland subduction zone. Connection between the Tonga and Vitiaz subduction segments until ca 20–15 Ma is predicted and agrees with tomography. Predicted average upper mantle and lower mantle sinking velocities are 3.3–7.0 cm/yr and 0.8–1.7 cm/yr, respectively, with variation occurring at different segments along the subduction zone owing to variation in subduction velocity and subduction partitioning. Our analysis couples plate tectonics to mantle evolution and demonstrates that reconstructions tied to an Indo-Atlantic moving hotspot reference frame better agree with mantle structure than those tied to a Pacific fixed hotspot reference fram

Geodynamic models of short-lived, long-lived and periodic flat slab subduction

© 2021 The Author(s). Published by Oxford University Press on behalf of The Royal Astronomical Society.Flat slab subduction has been ascribed to a variety of causes, including subduction of buoyant ridges/plateaus and forced trench retreat. The former, however, has irregular spatial correlations with flat slabs, while the latter has required external forcing in geodynamic subduction models, which might be insufficient or absent in nature. In this paper, we present buoyancy-driven numerical geodynamic models and aim to investigate flat slab subduction in the absence of external forcing as well as test the influence of overriding plate strength, subducting plate thickness, inclusion/exclusion of an oceanic plateau and lower mantle viscosity on flat slab formation and its evolution. Flat slab subduction is reproduced during normal oceanic subduction in the absence of ridge/plateau subduction and without externally forced plate motion. Subduction of a plateau-like feature, in this buoyancy-driven setting, enhances slab steepening. In models that produce flat slab subduction, it only commences after a prolonged period of slab dip angle reduction during lower mantle slab penetration. The flat slab is supported by mantle wedge suction, vertical compressive stresses at the base of the slab and upper mantle slab buckling stresses. Our models demonstrate three modes of flat slab subduction, namely short-lived (transient) flat slab subduction, long-lived flat slab subduction and periodic flat slab subduction, which occur for different model parameter combinations. Most models demonstrate slab folding at the 660 km discontinuity, which produces periodic changes in the upper mantle slab dip angle. With relatively high overriding plate strength or large subducting plate thickness, such folding results in periodic changes in the dip angle of the flat slab segment, which can lead to periodic flat slab subduction, providing a potential explanation for periodic arc migration. Flat slab subduction ends due to the local overriding plate shortening and thickening it produces, which forces mantle wedge opening and a reduction in mantle wedge suction. As overriding plate strength controls the shortening rate, it has a strong control on the duration of flat slab subduction, which increases with increasing strength. For the weakest overriding plate, flat slab subduction is short-lived and lasts only 6 Myr, while for the strongest overriding plate flat slab subduction is long-lived and exceeds 75 Myr. Progressive overriding plate shortening during flat slab subduction might explain why flat slab subduction terminated in the Eocene in western North America and in the Jurassic in South China

The future of Earth's oceans: consequences of subduction initiation in the Atlantic and implications for supercontinent formation

Subduction initiation is a cornerstone in the edifice of plate tectonics. It marks the turning point of the Earth's Wilson cycles and ultimately the supercycles as well. In this paper, we explore the consequences of subduction zone invasion in the Atlantic Ocean, following recent discoveries at the SW Iberia margin. We discuss a buoyancy argument based on the premise that old oceanic lithosphere is unstable for supporting large basins, implying that it must be removed in subduction zones. As a consequence, we propose a new conceptual model in which both the Pacific and the Atlantic oceans close simultaneously, leading to the termination of the present Earth's supercycle and to the formation of a new supercontinent, which we name Aurica. Our new conceptual model also provides insights into supercontinent formation and destruction (supercycles) proposed for past geological times (e.g. Pangaea, Rodinia, Columbia, Kenorland)