Global Bathymetry and Topography at 15 Arc Sec: SRTM15+

As the chronicle of plate motions through time, paleogeography is fundamental to our understanding of plate tectonics and its role in shaping the geology of the present-day. To properly appreciate the history of tectonics—and its influence on the deep Earth and climate—it is imperative to seek an accurate and global model of paleogeography. However, owing to the incessant loss of oceanic lithosphere through subduction, the paleogeographic reconstruction of ‘full-plates’ (including oceanic lithosphere) becomes increasingly challenging with age. Prior to 150 Ma ∼60% of the lithosphere is missing and reconstructions are developed without explicit regard for oceanic lithosphere or plate tectonic principles; in effect, reflecting the earlier mobilistic paradigm of continental drift. Although these ‘continental’ reconstructions have been immensely useful, the next-generation of mantle models requires global plate kinematic descriptions with full-plate reconstructions. Moreover, in disregarding (or only loosely applying) plate tectonic rules, continental reconstructions fail to take advantage of a wealth of additional information in the form of practical constraints. Following a series of new developments, both in geodynamic theory and analytical tools, it is now feasible to construct full-plate models that lend themselves to testing by the wider Earth-science community. Such a model is presented here for the late Paleozoic (410–250 Ma) together with a review of the underlying data. Although we expect this model to be particularly useful for numerical mantle modeling, we hope that it will also serve as a general framework for understanding late Paleozoic tectonics, one on which future improvements can be built and further tested.

Plate Tectonics in the Late Paleozoic

Global deep‐time plate motion models have traditionally followed a classical rigid plate approach, even though plate deformation is known to be significant. Here we present a global Mesozoic–Cenozoic deforming plate motion model that captures the progressive extension of all continental margins since the initiation of rifting within Pangea at ~240 Ma. The model also includes major failed continental rifts and compressional deformation along collision zones. The outlines and timing of regional deformation episodes are reconstructed from a wealth of published regional tectonic models and associated geological and geophysical data. We reconstruct absolute plate motions in a mantle reference frame with a joint global inversion using hot spot tracks for the last 80 million years and minimizing global trench migration velocities and net lithospheric rotation. In our optimized model, net rotation is consistently below 0.2°/Myr, and trench migration scatter is substantially reduced. Distributed plate deformation reaches a Mesozoic peak of 30 × 10^6 km^2 in the Late Jurassic (~160–155 Ma), driven by a vast network of rift systems. After a mid‐Cretaceous drop in deformation, it reaches a high of 48 x 10^6 km^2 in the Late Eocene (~35 Ma), driven by the progressive growth of plate collisions and the formation of new rift systems. About a third of the continental crustal area has been deformed since 240 Ma, partitioned roughly into 65% extension and 35% compression. This community plate model provides a framework for building detailed regional deforming plate networks and form a constraint for models of basin evolution and the plate‐mantle system.

A Global Plate Model Including Lithospheric Deformation Along Major Rifts and Orogens Since the Triassic

Seismic tomography: a window into deep Earth

Ensembles of numerical simulations are used in a variety of applications, such as meteorology or computational solid mechanics, in order to quantify the uncertainty or possible error in a model or simulation. Deriving robust statistics and visualizing the variability of an ensemble is a challenging task and is usually accomplished through direct visualization of ensemble members or by providing aggregate representations such as an average or pointwise probabilities. In many cases, the interesting quantities in a simulation are not dense fields, but are sets of features that are often represented as thresholds on physical or derived quantities. In this paper, we introduce a generalization of boxplots, called contour boxplots, for visualization and exploration of ensembles of contours or level sets of functions. Conventional boxplots have been widely used as an exploratory or communicative tool for data analysis, and they typically show the median, mean, confidence intervals, and outliers of a population. The proposed contour boxplots are a generalization of functional boxplots, which build on the notion of data depth. Data depth approximates the extent to which a particular sample is centrally located within its density function. This produces a center-outward ordering that gives rise to the statistical quantities that are essential to boxplots. Here we present a generalization of functional data depth to contours and demonstrate methods for displaying the resulting boxplots for two-dimensional simulation data in weather forecasting and computational fluid dynamics.

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Contour Boxplots: A Method for Characterizing Uncertainty in Feature Sets from Simulation Ensembles

GPlates is an open‐source, cross‐platform plate tectonic geographic information system, enabling the interactive manipulation of plate‐tectonic reconstructions and the visualization of geodata through geological time. GPlates allows the building of topological plate models representing the mosaic of evolving plate boundary networks through time, useful for computing plate velocity fields as surface boundary conditions for mantle convection models and for investigating physical and chemical exchanges of material between the surface and the deep Earth along tectonic plate boundaries. The ability of GPlates to visualize subsurface 3‐D scalar fields together with traditional geological surface data enables researchers to analyze their relationships through geological time in a common plate tectonic reference frame. To achieve this, a hierarchical cube map framework is used for rendering reconstructed surface raster data to support the rendering of subsurface 3‐D scalar fields using graphics‐hardware‐accelerated ray‐tracing techniques. GPlates enables the construction of plate deformation zones—regions combining extension, compression, and shearing that accommodate the relative motion between rigid blocks. Users can explore how strain rates, stretching/shortening factors, and crustal thickness evolve through space and time and interactively update the kinematics associated with deformation. Where data sets described by geometries (points, lines, or polygons) fall within deformation regions, the deformation can be applied to these geometries. Together, these tools allow users to build virtual Earth models that quantitatively describe continental assembly, fragmentation and dispersal and are interoperable with many other mapping and modeling tools, enabling applications in tectonics, geodynamics, basin evolution, orogenesis, deep Earth resource exploration, paleobiology, paleoceanography, and paleoclimate.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018GC007584

GPlates: Building a Virtual Earth Through Deep Time

We present a novel approach for visualizing the positional and geometrical variability of isosurfaces in uncertain 3D scalar fields. Our approach extends recent work by Pothkow and Hege [PH10] in that it accounts for correlations in the data to determine more reliable isosurface crossing probabilities. We introduce an incremental updatescheme that allows integrating the probability computation into front-to-back volume ray-casting efficiently. Our method accounts for homogeneous and anisotropic correlations, and it determines for each sampling interval along a ray the probability of crossing an isosurface for the first time. To visualize the positional and geometrical uncertainty even under viewing directions parallel to the surface normal, we propose a new color mapping scheme based on the approximate spatial deviation of possible surface points from the mean surface. The additional use of saturation enables to distinguish between areas of high and low statistical dependence. Experimental results confirm the effectiveness of our approach for the visualization of uncertainty related to position and shape of convex and concave isosurface structures.

Visualizing the positional and geometrical variability of isosurfaces in uncertain scalar fields

Visualizing correlations, i.e., the tendency of uncertain data values at different spatial positions to change contrarily or according to each other, allows inferring on the possible variations of structures in the data. Visualizing global correlation structures, however, is extremely challenging, since it is not clear how the visualization of complicated long-range dependencies can be integrated into standard visualizations of spatial data. Furthermore, storing correlation information imposes a memory requirement that is quadratic in the number of spatial sample positions. This paper presents a novel approach for visualizing both positive and inverse global correlation structures in uncertain 2D scalar fields, where the uncertainty is modeled via a multivariate Gaussian distribution. We introduce a new measure for the degree of dependency of a random variable on its local and global surroundings, and we propose a spatial clustering approach based on this measure to classify regions of a particular correlation strength. The clustering performs a correlation filtering, which results in a representation that is only linear in the number of spatial sample points. Via cluster coloring the correlation information can be embedded into visualizations of other statistical quantities, such as the mean and the standard deviation. We finally propose a hierarchical cluster subdivision scheme to further allow for the simultaneous visualization of local and global correlations. © 2012 Wiley Periodicals, Inc.

Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields

In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data. It does not, however, allow inferring on the effect of uncertainty on differential quantities such as the gradient, which depend on the variability of the rate of change of the data. Analyzing the variability of gradients is nonetheless more complicated, since, unlike scalars, gradients vary in both strength and direction. This requires initially the mathematical derivation of their respective value ranges, and then the development of effective analysis techniques for these ranges. This paper takes a first step into this direction: Based on the stochastic modeling of uncertainty via multivariate random variables, we start by deriving uncertainty parameters, such as the mean and the covariance matrix, for gradients in uncertain discrete scalar fields. We do not make any assumption about the distribution of the random variables. Then, for the first time to our best knowledge, we develop a mathematical framework for computing confidence intervals for both the gradient orientation and the strength of the derivative in any prescribed direction, for instance, the mean gradient direction. While this framework generalizes to 3D uncertain scalar fields, we concentrate on the visualization of the resulting intervals in 2D fields. We propose a novel color diffusion scheme to visualize both the absolute variability of the derivative strength and its magnitude relative to the mean values. A special family of circular glyphs is introduced to convey the uncertainty in gradient orientation. For a number of synthetic and real-world data sets, we demonstrate the use of our approach for analyzing the stability of certain features in uncertain 2D scalar fields, with respect to both local derivatives and feature orientation.

Visualizing the Variability of Gradients in Uncertain 2D Scalar Fields

Overlaid plots of iso-contours in individual members of a scalar ensemble field are a popular concept to visualize the data uncertainty. However, such plots do not allow inferring on the spatial cumulative probability distribution of the iso-contours, and they cannot reveal distribution characteristics like spread and topology for very large amounts of contours. In this paper, we propose a new visualization technique for iso-contours in ensemble data sets to overcome these limitations. Our technique makes no assumption about a stochastic uncertainty model, rendering it suitable for arbitrary ensemble distributions. It computes a statistical summary of the ensemble over the spatial domain, including probability density values for arbitrary domain points. From this information, the uncertainty and topology of iso-contours can be determined, as well as the variations in gradient magnitude around these contours. Since the visualization is carried out on the GPU, our approach allows analyzing even very large ensemble data sets at interactive rates.

Tobias Pfaffelmoser

Papers

GPlates: Building a Virtual Earth Through Deep Time

Visualizing the positional and geometrical variability of isosurfaces in uncertain scalar fields

Visualization of Global Correlation Structures in Uncertain 2D Scalar Fields

Visualizing the Variability of Gradients in Uncertain 2D Scalar Fields

Visualizing Contour Distributions in 2D Ensemble Data