Abstract
Abstract. Image correlation techniques have provided new ways to analyse the distribution of deformation in analogue models of tectonics in space and time. Here, we demonstrate, using a new version of our software package (TecPIV), how the correlation of successive time-lapse images of a deforming model allows not only to evaluate the components of the strain-rate tensor at any time in the model but also to calculate the finite displacements and finite strain tensor. We illustrate with synthetic images how the algorithm produces maps of the velocity gradients, small-strain tensor components, incremental or instantaneous principal strains and maximum shear. The incremental displacements can then be summed up with Eulerian or Lagrangian summation, and the components of the 2-D finite strain tensor can be calculated together with the finite principal strain and maximum finite shear. We benchmark the measures of finite displacements using specific synthetic tests for each summation mode. The deformation gradient tensor is calculated from the deformed state and decomposed into the finite rigid-body rotation and left or right finite-stretch tensors, allowing the deformation ellipsoids to be drawn. The finite strain has long been the only quantified measure of strain in analogue models. The presented software package allows producing these finite strain measures while also accessing incremental measures of strain. The more complete characterisation of the deformation of tectonic analogue models will facilitate the comparison with numerical simulations and geological data and help produce conceptual mechanical models.
Highlights
The concept of physical similarity rests on the idea that multiple physical systems may share the same underpinning physical laws (Sterrett, 2009, 2017a, b, and references therein).In Earth sciences, scaled models have been employed for over a century to test hypotheses on the driving mechanisms of tectonic processes derived from, and constrained by, a variety of geological and geophysical data (e.g. Koyi, 1997; Ranalli, 2001; Graveleau et al, 2012, and references therein)
For the purpose of facilitating the particle imaging velocimetry (PIV) analysis of analogue models of tectonics, we developed TecPIV, a MATLAB software package allowing, within a single interface, to calibrate and correct the views of the model, correlate the successive images and produce image outputs with incremental displacements and their spatial derivatives (Boutelier, 2016)
Particle imaging velocimetry of analogue models of tectonics can be performed with inexpensive, high-resolution commercial DSLR cameras and open-sourced scripts for MATLAB
Summary
The concept of physical similarity rests on the idea that multiple physical systems may share the same underpinning physical laws (Sterrett, 2009, 2017a, b, and references therein). Adam et al, 2005, 2013; Schrank et al, 2008; Rosenau et al, 2009; Saumur et al, 2015; Boutelier et al, 2014; Boutelier and Cruden, 2017, 2018; Kavanagh et al, 2015, 2017; Zwaan et al, 2018; Dooley et al, 2018; Rudolf et al, 2019). Lower sampling rates can be used, allowing the use of less expensive, higher-resolution (up to 50 Mpixels) consumer-grade digital cameras (DSLRs) to capture sufficient light during the long exposure time We acknowledge that such an approach is not satisfactory for analogue tectonic models that may include rapid displacements, such as the models of seismic rupture
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