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. The different scales include: Plate Regional Outcrop Hand-sample Grain
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.