Particle image velocimetry (PIV), a method based on image cross-correlation, is widely used for obtaining velocity fields from time-series of images of deforming objects. Rather than instantaneous velocities, we are interested in reconstructing cumulative deformation, and use PIV-derived incremental displacements for this purpose. Our focus is on analogue models of tectonic processes, which can accumulate large deformation. Importantly, PIV provides incremental displacements during analogue model evolution in a spatial reference (Eulerian) frame, without the need for explicit markers in a model. We integrate the displacements in a material reference (Lagrangian) frame, such that displacements can be integrated to track the spatial accumulative deformation field as a function of time. To describe cumulative, finite deformation, various strain tensors have been developed, and we discuss what strain measure best describes large shape changes, as standard infinitesimal strain tensors no longer apply for large deformation. PIV or comparable techniques have become a common method to determine strain in analogue models. However, the qualitative interpretation of observed strain has remained problematic for complex settings. Hence, PIV-derived displacements have not been fully exploited before, as methods to qualitatively characterize cumulative, large strain have been lacking. Notably, in tectonic settings, different types of deformation-extension, shortening, strike-slip-can be superimposed. We demonstrate that when shape changes are described in terms of Hencky strains, a logarithmic strain measure, finite deformation can be qualitatively described based on the relative magnitude of the two principal Hencky strains. Thereby, our method introduces a physically meaningful classification of large 2-D strains. We show that our strain type classification method allows for accurate mapping of tectonic structures in analogue models of lithospheric deformation, and complements visual inspection of fault geometries. Our method can easily discern complex strike-slip shear zones, thrust faults and extensional structures and its evolution in time. Our newly developed software to compute deformation is freely available and can be used to post-process incremental displacements from PIV or similar autocorrelation methods.

Stress-dependent nonlinear upper mantle rheology has a firm base in rock mechanical tests, where this nonlinearity results from dislocation creep of minerals. In the last few decades there has been some attention to nonlinear, power-law, materials for application in scaled analogue experiments for tectonic processes. However, studies describing the rheology of analogue materials with the same nonlinear dependency on stress as observed for lithospheric mantle materials at relevant stress levels, are still lacking. In this study we have developed and rheologically tested materials based on combinations of silicone polymers and plasticine, with the aim of obtaining a material that can serve as a laboratory analogue to the power-law rheology of olivine aggregates at lithospheric mantle conditions. From our steady-state creep tests we find that it is possible to obtain such a power-law material, with effective viscosities over relevant model stress ranges [5–4000 Pa] that allow for nonlinear deformation at laboratory time scales. We apply the developed material to a process where localized deformation of the lithosphere can be expected: slab break-off. We study this process using analogue models, where we apply the new nonlinear material to the lithospheric mantle domains, while we use Newtonian glucose to represent the low viscous asthenosphere. Now that we properly manage power-law behavior in our analogue lithosphere materials, we are able to model localized lithospheric tearing.

The sea floor of intraslope minibasins on passive continental margins plays a significant role in controlling turbidity current pathways and the resulting sediment distribution. To address this, laboratory analogue modelling of intraslope minibasin formation is combined with numerical flow simulations of multi-event turbidity currents. This approach permits an improved understanding of evolving flow–bathymetry–deposit interactions and the resulting internal stacking patterns of the infills of such minibasins. The bathymetry includes a shelf to slope channel followed by an upper minibasin, which are separated by a confining ridge from two lower minibasins that compares well with analogous bathymetries reported from natural settings. From a wider range of numerical flow experiments, a series of 100 consecutive flows is reported in detail. The turbidity currents are released into the channel and upon reaching the upper minibasin follow a series of stages from short initial ponding, ‘filling and spilling’ and an extended transition to long retrogradational ponding. Upon reaching the upper minibasin floor, the currents undergo a hydraulic jump and therefore much sediment is deposited in the central part of the minibasin and the counterslope. This modifies the bathymetry such that in the fill and spill stage, flow stripping and grain-size partitioning cause some finer sediment to be transported across the confining ridge into the lower minibasins. Throughout the basin infill process, the sequences retrograde upstream, accompanied by lateral switching into locally formed depressions in the upper minibasin. After the fill and spill stage, significant deposition occurs in the channel where retrograding cyclic steps with wavelengths of 1 to 2 km develop as a function of pulsating flow criticality. These results are at variance with conventional schemes that emphasize sequential downstream minibasin filling through ponding dominated by vertical aggradation. Comparison of these results with published field and experimental examples provides support for the main conclusions.