THE MULTISCALE NATURE OF DEFORMATION
AND METAMORPHISM
THE MULTISCALE NATURE OF DEFORMATION
AND METAMORPHISM
AND METAMORPHISM
Data, Patterns, Dynamics, Prediction
Data, Patterns, Dynamics, Prediction
Alison Ord
Mentor: Flip Phillips
Background
Background
is concerned with the processes that operate during the deformation and metamorphism of rocks in the crust and upper lithosphere of the Earth. The deformation and metamorphism of rocks involves structural rearrangements of elements of the rock at the microscale by processes such as mass diffusion, dislocation slip and climb, grain-boundary migration and fracturing at the same time as chemical reactions proceed. In some instances infiltrating fluids introduce or remove chemical components and may influence mechanical properties through changes in mineralogical composition, fluid pressure or temperature. At the same time, heat is added to or removed from the system depending on the surrounding tectonic environment. Such mechanisms do not operate independently of each other but are coupled so that each process has feedback influences on the others leading to structures and mineral assemblages that do not develop in the uncoupled environment.
Its contents are represented by this Word Cloud.
This computational essay is a first step towards developing the application of the tools of nonlinear dynamics to measuring rocks, to measuring the structural architectures which result from processes interacting and developing in a coupled environment.
Vision
Vision
The vision for Mathematica is of moving a cursor through coordinates for the surface of a deformed, folded rock and to watch data driven analyses change in different windows including: spatial attractors, wavelet transforms, singularity spectra, Hurst exponents, recurrence plots (including the ability for cross—and joint—recurrence plots and their quantitative analysis), Fourier transforms, recurrence histograms, networks, and sparsely determined nonlinear determinations of the differential equations describing the data.
(x,y,z)
Step 1
Step 1
Are folded rocks a snapshot of a nonlinear dynamic system? When layered rocks are shortened during tectonic events, the most obvious structures formed are folds. Folding of layered rocks causes a change in geological structure that can lead to a fundamental modification of the mechanical and hydraulic properties of the rock mass across several orders of magnitude in length—typically from the millimetre to the kilometre-scale.
The understanding of how, why and on which scale folding occurs therefore has fundamental implications for problems in geology and engineering, including prediction of the form and location of hydrocarbon accumulations, salt domes, groundwater flow, mineralization, and rock slope stability.
We have prepared three dimensional models of natural fold systems using photogrammetry and we explore the multifractal geometry using wavelet transforms and recurrence quantification in order to delineate the dynamics of naturally folded systems.
The Data
The Data
Surfaces of folded rocks
Surfaces of folded rocks
First we see a multiply deformed rock with porphyroblasts from Rum Jungle in Australia.
It is then photographed from multiple angles, and the images collated and analysed within CloudCompare. This image shows interpreted cloud of points, with a single line through the points denoting the data collected, and shown in cross section in the following figure.
Here is another multiply folded rock, this time from Broken Hill in Australia. First, we look at the rock, sitting on a structured page used for collating the photographic images.
Second, we see the cloud of points for that system, derived from the photo collection.
Third, we have the cloud of points just of the rock, followed by a section through the rock cloud.
The Analyses
The Analyses
Acknowledgments
Acknowledgments
I thank Flip Phillips and Paul Abbott for supporting my tentative steps towards incorporating the tools of nonlinear dynamics into Wolfram Language for creative application to understanding how rocks deform. I thank Stephen Wolfram and the Wolfram Summer School community, including mentors, staff, TA’s, and of course my fellow students for an intense, productive and very happy 3 weeks.