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.

Large-scale strike-slip faults are associated with significant strain partitioning in releasing/restraining bends and often display map-view curvatures ending in horse-tail geometries. Such faults are commonly associated with indentation tectonics, where shortening in front of indenters is transferred laterally to transpression, strike-slip and the formation of transtensional/extensional basins. We investigate how these structurally distinct domains are kinematically linked by the means of a crustal-scale analogue modelling approach where a deformable crust is moved against a stable and rigid indenter. The modelling demonstrates that the geometry of the indenter is the major controlling parameter driving strain partitioning and deformation transfer from thrusting and transpression to strike-slip and transtension, whereas the rotation of the mobile plate controls the opening of triangular shaped transtensional basins. Flow of the ductile crust leads to the distribution of deformation over a wider area, facilitating strike-slip splaying into transtension/extension behind the indenter. Our results show a very good correlation with the Moesian indentation in the Carpatho-Balkanides system of South-Eastern Europe, where strain is partitioned around the dextral Cerna and Timok strike-slip faults and transferred to thrusting in the Balkanides part of the Moesian indenter and to transtension/extension in the neighbouring South Carpathians.