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The Earth's crust is exposed by tectonic processes and is not static over time. Modelling of the Earth's surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth's surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties. [ABSTRACT FROM AUTHOR]

Plate tectonics theory, established in the 1960s, has been successful in explaining many geological phenomena, processes and events that occurred in the Phanerozoic. However, the theory has often struggled to provide a coherent framework in interpreting geological records in continental interior and Precambrian period. In dealing with the relationship between plate tectonics and continental geology, continental interior tectonics was often separated from continental margin tectonics in the inheritance and development of their structure and composition. This separation led to the illusion that the plate tectonics theory is not applicable to Precambrian geology, particularly in explaining the fundamental geological characteristics of Archean cratons. Although this illusion does not mean that the Archean continental crust did not originate from a regime of plate tectonics, it led to the development of alternative tectonic models, often involving vertical movements under a regime of stagnant lid tectonics, including not only endogenous processes such as gravitational sagduction, mantle plumes and heat pipes but also exogenous processes such as bolide impacts. These vertical processes were not unique to the Archean but persisted into the Phanerozoic. They result from mantle poloidal convection at different depths, not specific to any particular period. Upgrading the plate tectonics theory from the traditional kinematic model in the 20th century to a holistic kinematic-dynamic model in the 21st century and systematically examining the vertical transport of matter and energy at plate margins, it is evident that plate tectonics can explain the common geological characteristics of Archean cratons, such as lithological associations, structural patterns and metamorphic evolution. By deciphering the structure and composition of convergent plate margins as well as their dynamics, the formation and evolution of continental crust since the Archean can be divided into ancient plate tectonics in the Precambrian and modern plate tectonics in the Phanerozoic. In addition, there are the following three characteristic features in the Archean: (1) convective mantle temperatures were 200–300°C higher than in the Phanerozoic, (2) newly formed basaltic oceanic crust was as thick as 30–40 km, and (3) the asthenosphere had a composition similar to the primitive mantle rather than the depleted mantle at present. On this basis, the upgraded plate tectonics theory can successfully explain the major geological phenomena of Archean cratons. This approach provides a new perspective on and deep insights into the evolution of early Earth and the origin of continental crust. In detail, Archean tonalite-trondhjemite-granodiorite (TTG) rocks would result from partial melting of the over-thick basaltic oceanic crust at convergent plate margins. The structural patterns of gneissic domes and greenstone keels would result from the buoyancy-driven emplacement of TTG magmas and its interaction with the basaltic crust at convergent margins, and komatiites in greenstone belts would be the product of mantle plume activity in the regime of ancient plate tectonics. The widespread distribution of high-grade metamorphic rocks in a planar fashion, rather than in zones, is ascrible to separation of the gneissic domes from the greenstone belts. The shortage of calc-alkaline andesites in bimodal volcanic associations suggests the shortage of sediment accretionary wedges derived from weathering of granitic continental crust above oceanic subduction zones. The absence of Penrose-type ophiolites suggests that during the subduction initiation of microplates, only the upper volcanic rocks of the thick oceanic crust were offscrapped to form basalt accretionary wedges. The absence of blueschist and eclogite as well as classic paired metamorphic belts suggests that convergent plate margins were over-thickened through either warm subduction or hard collision of the thick oceanic crust at moderate geothermal gradients. Therefore, only by correctly recognizing and understanding the nature of Archean cartons can plate tectonics reasonably explain their fundamental geological characteristics. [ABSTRACT FROM AUTHOR]