Advanced Structural Analysis : Quantitative and Multiscale Analysis

Abstract

This online course on Advanced Structural Geology is intended for senior undergraduate students and graduate students of solid earth sciences. The course consists of the following four Sessions covering modern developments of Structural Geology in the areas of: 1) Quantitative Geometrical Analysis, 2) Rheology and Deformation Mechanisms, 3) Quantitative Kinematic Analysis, and 4) Introduction to Micromechanics and Multiscale Analysis. Session 1 builds on traditional orientation analysis for linear and planar fabric elements covered in landmark textbooks of structural geology. We show that these fabrics can be readily dealt with by unit vectors. However, most fabrics in rocks including the shape and lattice orientations of the constituent elements and grains are defined by 3D elements. The orientation of such fabric elements must be defined by a set of Euler angles or equivalently an orientation matrix. Statistic analysis of 3D orientation data is introduced and associated numerical techniques are discussed using mathematics applications MATLAB and MathCad. Session 2 presents the fundamental concepts of mechanics at a level required for Sessions 3 and 4. This session also prepared the students for the research literature in solid earth sciences. The concepts of multiscale stress, multiscale strain, non-linear rheology, and related partitioning and homogenization are introduced at a primary level. Deformation mechanisms, lattice preferred orientation development, and rheological anisotropy are discussed. These concepts will be revisited in Sessions 3 and 4 at a more advanced level, Session 3 is devoted to the kinematics of continuous deformation. This provides the students with the knowledge and skill set necessary for understanding progressive, large-strain deformations of rocks that are responsible for the formation of fabrics. The two-state description of finite deformation is given first and the instantaneous description of flow second. The kinematic modeling work of tabular high-strain zones, from the seminal work of J.G. Ramsay and Graham in 1970 till the end of last century, is reviewed and summarized in this session. Session 4 is devoted to recent advances on multiscale analysis and a complete mechanics approach to Structural Geology. These advances tackles the major challenge in Structural Geology, namely how to bridge the scale gap between observations and the tectonic boundary conditions. As our observations are most commonly made on scales much smaller than the tectonic problem of interest, and that our observations are inevitably discontinuous, a multiscale approach is necessary. This session provides the basic theoretical background and numerical resource for a self-consistent multiscale approach based on micromechanics. The goal is to introduce the principles and encourage students to read the lecture notes and related papers if they tackle multiscale geology problems.