Week 4

Question 1

Vectors - properties

Answer 1

Have a magnitude and orientation (1st order tensors)

= can resolve

Question 2

Position vector =

Answer 2

location of point w.r.t references axes

Question 3

Issues with the Flinn plot

Answer 3

:) Type and magnitude of finite strain

:( How strain varies spatially
:( Rotational component of strain

Question 4

e=

Answer 4

(ld-lo)/lo

Question 5

Graph of displacement, u (y) vs original position, X (x)

Answer 5

Gradient = /\u / /\X

= e

(With some experimental area)

Question 6

Absolute displacement vector

Answer 6

Initial and final positions known

Question 7

Relative displacement vector

Answer 7

Measured relative to fixed regional reference e.g. GPS velocity fields

Question 8

Local displacement vector

Answer 8

Measured relative to single point(s) e.g. strain ellipsoid

Question 9

Incremental and infinitesimal strain

Answer 9

Can show different results to finite strain

GPS velocity fields = mm/cm scale over 100s km
- measure over time = rates

Question 10

Basin and Range

Answer 10

= province in western N America

Crust and upper mantle undergoing extension since Cenozoic (Eocene)

Extension = prominent fault scarps (“ranges”) and depressions (“basins”)

Question 11

Importance of displacement vectors

Answer 11

/\u//\X = e

Systematic analysis of displacement vectors in 2/3D = SPATIAL variability (i.e. how strain varies with X) and ROTATIONAL component of strain

Question 12

How to determine compression/extension from GPS velocities

Answer 12

e.g. if GPS velocities are pointing E-W

• look at values for stations in E
• look at values for stations in W
• which side is experiencing greater GPS velocities?
• i.e. are they getting further apart from each other or closer?

Question 13

How could extension occur in a subduction zone?

Answer 13

Slip along subduction interface during e.g. an earthquake may have released elastic strains that had built up in the overriding plate during the pre-seismic period = extension

Question 14

How could you produce a graph of displacement, u (y) vs original position, X (x) in a tectonic context?

Answer 14

u = Ueast (displacements to east)

X = easting

N.B. Make sure units are consistent

Can show how the displacement gradient i.e. EXTENSION increases/decreases across a region

Question 15

Overall deformation parameters

Answer 15

Instantaneous stretching axes (ISA)

Flow apophyses

Vorticity number (Wk)

Question 16

Overall deformation parameters; ISA

Answer 16

Directions of max and min (fastest and slowest) stretching

Bisects fields of infinitesimal contraction and extension

Question 17

Overall deformation parameters; flow apophyses

Answer 17

Separate different fields of flow/different domains of particle paths

Coaxial strain = orthogonal (90)

Simple shear = //

Subsimple shear = oblique (60)

Angles = alpha

Question 18

Overall deformation parameters; vorticity number Wk

Answer 18

= cosalpha (from flow apophyses)

Describes how fast a particle is rotating if it was embedded in a soft medium

Question 19

Requirements for strain from stress/stress from strain

Answer 19

Linear viscous rheology (Newtonian)

Homogeneous medium without pre-existing deformation boundaries

If orientation of deformation boundaries known may be possible to relate stresses to ISAs