Introduction

1. Introduction Stress versus strain: The two most important terms used throughout this course are STRESS and STRAIN. What structural geologists actually observe and directly measure is strain. Stresses, on the other hand, are not directly measured, but in principal they may be inferred or constrained from the strain.

2. Introduction Brittle versus ductile: Generally, rocks respond to stress in one of two ways: they break, or they bend. Brittle deformation: when the rock breaks. Examples for brittle deformation include: • Faults • Joints • Dikes

3. Introduction Ductile deformation: when rocks bend or flow. Examples for ductile deformation include: • Foliation and lineation • Mylonite • Boudinage

4. Introduction Question: Under what conditions do rocks exhibit ductile/brittle behavior? Rocks undergo ductile deformation when subjected to high confining pressure and temperature. Thus, brittle structures form near the surface and in the upper crust, and ductile structures form at greater depth.

5. Introduction A fault near the surface becomes mylonite at great depth:

6. Introduction The kink band structure shown below is an example for brittle ductile deformation:

7. Introduction Time scales: geological processes occur over a wide range of characteristic time scales. What are the characteristic time scales for fault rupture? Stresses that accumulate steadily over many years, due to relative plate motion, may be released abruptly within seconds to tens of seconds.

8. Introduction What are the characteristic time scales for dike intrusion? Modern dikes eruptions (e.g., in Hawaii) have lasted between a few hours and a few days (show a movie). What are the characteristic time scales for mylonite formation? The physical processes that accompany the formation of metamorphic fabric are slow (e.g., dissolution and re-precipitation of minerals).

9. Introduction While the formation of brittle structures is discontinuous and evolves via abrupt steps, the formation of ductile fabric is more or less continuous and is governed by slow processes. • Length scales: deformation is occurring simultaneously at a wide range of length scales. • The different scales include: • Plate • Regional • Outcrop • Hand-sample • Grain • Crystal Figure from Allmendinger’s lecture notes

10. Introduction A few slides back you have seen a picture of mylonite at the scale of an outcrop. This is how it may look at the scale of a few crystals or grains:

11. Introduction Question: How long is the coast of Britain? It turned out that the answer to that question depends on the ruler's length. figure from Wikepedia

12. Introduction On a log-log scale we get: A power-law function provides good fit to the data: which is equivalent to: The b exponent is known as the fractal dimension.

13. Introduction Fractals are very common in nature: cauliflower lightning leaf Drainage system

14. Introduction Fault population too are fractals:

15. Introduction Fractal dimension of faults in Japan has been determined using the box-counting algorithm [from Hirata, 1989]

16. Introduction Frequency-length distribution for normal faults on the plain of Venus obtained from a Magellan SAR image (from Scholz, 1997).

17. Introduction Cumulative length distribution of sub-faults of the San Andreas fault (from Scholz, 1998).

18. Introduction Map of faults and joints exposed in the Yucca Mt. (from Barton, 1995). Note that small joints are more abundant than large ones.