introduction stress versus strain: the two most important terms used throughout this course are...

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.

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

Introduction

Ductile deformation: when rocks bend or flow. Examples for ductile deformation include:

• Foliation and lineation• Mylonite• Boudinage

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.

Introduction

A fault near the surface becomes mylonite at great depth:

Introduction

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

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.

Introduction

What are the characteristic time scales for mylonite formation?

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 dike intrusion?

The physical processes that accompany the formation of metamorphic fabric are slow (e.g., dissolution and re-precipitation of minerals).

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

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:

Introduction

Question: How long is the coast of Britain?

It turned out that the answer to that question depends on the ruler's length.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

figure from Wikepedia

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.€

length = a× scale−b ,

€

log(length) = a' −b log(scale).

Introduction

Fractals are very common in nature:

leaf

cauliflower lightning

Drainagesystem

Introduction

Fault population too are fractals:

Introduction

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

Introduction

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

Introduction

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

Introduction

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