# Chapter 5

## Deformation and Flow

Structural geologists think about deformation and flow as an inverse problem: from the current state back towards some (undeformed) initial state. For example, the lower right photograph in the frontispiece for this chapter shows deformed oöids with elliptical shapes: ratios of long to short axes are about 1.56 (Cloos, 1947, 1971). The upper left photograph shows nearly undeformed oöids with approximately circular shapes: ratios of long to short axes are about 1.16. One can think of the deformed oöids being transformed back towards an initial state much like that of the nearly undeformed oöids. Considerable insight can be obtained from the formulation of a forward problem. Field observations of many sorts, including the deformed shapes of objects such as oöids, may be selected to constrain a forward model built upon a synthesis of controlled laboratory experimental data on the behavior of rock materials and theoretical investigations of deformation and failure.

## Exercises

### Concepts from Chapter 5

These exercises explore concepts from Chapter 5 including the estimation of principal stretches from deformed objects in rock, the characteristics of uniaxial and biaxial extension, pure dilation, and simple shearing, and an evaluation of the conditions under which strain may be approximated as infinitesimal.

### Belemnite stretch at Morcles Nappe

The maximum and minimum stretches in the plane of a slaty cleavage are estimated from measurements of deformed belemnite guards within the Liassic slate of the Morcles Nappe at Leytron, Valais, Switzerland. This exercise uses data found in the belemnite.txt file.

### Infinitesimal strain during the great San Francisco earthquake

An elementary mechanical model is used to explore the relationship between slip on a strike-slip fault and the strain of nearby rocks. Geodetic data from the Pt. Arena area is used to estimate the depth of slip on the San Andreas Fault during the 1906 earthquake and to calculate the strain. This exercise uses data found in the arena_data.txt file.

## Figures

The following button links to a folder in Box where images from the text and images that are supplementary to those found in the text live.

## Scripts

The following button links to a folder in Box where MATLAB scripts (.m) geared for the MATLAB editor live.