SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so‐called ‘sticky air’ approach has gained interest as a free‐surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosity fluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostatic relaxation of a cosine perturbation and (2) topography changes above a rising plume. We quantitatively compare topographies calculated by six different numerical codes (using finite difference and finite element techniques) using three different topography calculation methods: (i) direct calculation of topography from normal stress, (ii) body‐fitting methods allowing for meshing the topography and (iii) Lagrangian tracking of the topography on an Eulerian grid. It is found that the sticky air approach works well as long as the term (ηst/ηch)/(hst/L)3 is sufficiently small, where ηst and hst are the viscosity and thickness of the sticky air layer, and ηch and L are the characteristic viscosity and length scale of the model, respectively. Spurious lateral fluctuations of topography, as observed in some marker‐based sticky air approaches, may effectively be damped by an anisotropic distribution of markers with a higher number of markers per element in the vertical than in the horizontal direction.

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Abstract:We report results of a study comparing numerical models of sandbox-type experiments. Two experimental designs were examined: (1) A brittle shortening experiment in which a thrust wedge is built in material of alternating frictional strength; and (2) an extension experiment in which a weak, basal viscous layer affects normal fault localization and propagation in overlying brittle materials. Eight different numerical codes, both commercial and academic, were tested against each other. Our results show that: (1) The overall evolution of all numerical codes is broadly similar. (2) Shortening is accommodated by in-sequence forward propagation of thrusts. The surface slope of the thrust wedge is within the stable field predicted by critical taper theory. (3) Details of thrust spacing, dip angle and number of thrusts vary between different codes for the shortening experiment. (4) Shear zones initiate at the velocity discontinuity in the extension experiment. The asymmetric evolution of the models is similar for all numerical codes. (5) Resolution affects strain localization and the number of shear zones that develop in strain-softening brittle material. (6) The variability between numerical codes is greater for the shortening than the extension experiment.Comparison to equivalent analogue experiments shows that the overall dynamic evolution of the numerical and analogue models is similar, in spite of the difficulty of achieving an exact representation of the analogue conditions with a numerical model. We find that the degree of variability between individual numerical results is about the same as between individual analogue models. Differences among and between numerical and analogue results are found in predictions of location, spacing and dip angle of shear zones. Our results show that numerical models using different solution techniques can to first order successfully reproduce structures observed in analogue sandbox experiments. The comparisons serve to highlight robust features in tectonic modelling of thrust wedges and brittle-viscous extension.Numerical and analogue modelling methods represent two different techniques with which the evolution of geological structures, such as fold-and-thrust belts and sedimentary basins, can be investigated. The underlying assumption with both methods is that their results approximate the development of structures in the real Earth in a reasonable manner. We may then expect that the results of analogue and numerical models look similar when applied to the same (2) to test the similarity of numerical and analogue models, in order to help establish robust features of tectonic models on the scale of the upper crust.The companion paper (Schreurs et al. 2006) presents the results of an analogue comparison study with ten participating modelling laboratories. Two experimental set-ups were tested: (1) a brittle convergent thrust wedge experiment and (2) a brittle-viscous extension experiment. The reproducibility of modelling results between the laboratories was found to be fai...

Continental rifts often develop from linkage of distinct rift segments under varying degrees of extension obliquity. These rift segments arise from rift initiation at non-aligned crustal heterogeneities and need to interact to develop a full-scale rift system. Here, we test the effects of 1) oblique extension and 2) initial heterogeneity (seed) offset on continental rift interaction with the use of an improved analogue model setup. X-Ray computer tomography (CT) techniques are used to analyse the 3D models through time and the results are compared with additional numerical models and natural examples. The experimental results reveal that increasing extension obliquity strongly changes rift segment structures from wide rifts in orthogonal settings to narrower rifts with oblique internal structures under oblique extension conditions to narrow strike-slip dominated systems towards the strike-slip domain. We also find that both decreasing seed offset and increasing extension obliquity promote hard linkage of rift segments through the formation of continuous rift boundary faults at the surface. (Initial) soft linkage through the formation of relay ramps is more likely when seed offset increases or extension is more orthogonal. Rather than linking at depth, the rift boundary faults curve around each other at depth and merge towards the surface to form a continuous trough. Orthogonal extension promotes the formation of intra-rift horsts, which may provide hydrocarbon traps in nature.

: We report a direct comparison of scaled analogue experiments to test the reproducibility of model results among ten different experimental modelling laboratories. We present results for two experiments: a brittle thrust wedge experiment and a brittleviscous extension experiment. The experimental set-up, the model construction technique, the viscous material and the base and wall properties were prescribed. However, each laboratory used its own frictional analogue material and experimental apparatus. Comparison of results for the shortening experiment highlights large differences in model evolution that may have resulted from (1) differences in boundary conditions (indenter or basal-pull models), (2) differences in model widths, (3) location of observation (for example, sidewall versus centre of model), (4) material properties, (5) base and sidewall frictional properties, and (6) differences in set-up technique of individual experimenters. Six laboratories carried out the shortening experiment with a mobile wall. The overall evolution of their models is broadly similar, with the development of a thrust wedge characterized by forward thrust propagation and by back thrusting. However, significant variations are observed in spacing between thrusts, their dip angles, number of forward thrusts and back thrusts, and surface slopes. The structural evolution of the brittle-viscous extension experiments is similar to a high degree. Faulting initiates in the brittle layers above the viscous layer in