The deformation in the Plate Boundary zones

Shear Zone : San Andreas

-

Frédéric Flerit

The geometry of the Plates, and their position

Three kind of ocean plate boundary

Tectonics

The Pa-NA Boundary Zone

TOPOGRAPHYFault SYSTEM

Motion of

Pa/NA

The NAF offsets the geology features : 200km

100 km

The NAF Offsets mountain ranges

The NAF Offsets rivers : 100m – 1km

200 m200 m

200 m

200 m

… m

Long term deformation : lateral offsets at all scales

PA

NA

The plates are rigid and they are separated by plastic faults

Two historical major Earthquakes

1906 San Andreas 1857 Big bend

average slip of 6 m.

1906 San Andreas Eq 6m of lateral offset

The NAF Offset orange trees rows : 6 m

The profile of the co seismic displacement measured on the triangulation network of California

(Reid 1910)

100 km

SouthCalifornia

San Andreas Big Bend San Andreas south

Los AngelesLos Angeles

The velocity profile assoiated with the Plate motion

PA

NA

100 km

How to reconcile the Long term deformation with the deformation produced by an earthquake ?

The concept of Seismic Cycle

Two phases

1) interseismic loading

2) Coseismic relaxation

The seismic cycle

Consequence : The crust is elastic (load / relaxation)And the faults in the crust are plastic(permanent deformation)

The concept of Locking depth

Seismic

-

Brittle

(10-20 km)

Aseismic

-

Ductile

The velocity profile

Associated with the

Locking depth : d

Problems

Draw three profiles of the velocity vectors across SAF?

How can we invert the locking depth of the SAF (depth of the transition brittle-ductile) ?

Draw a profile of the velocity vectors parallel to the SAF.

Define the Azimut of the Pa/NA plate motion in Los Angeles Region, What is the Azimut of The SAF ?

What can you tell about the components of GPS velocity vectors perpendicular to the Pa/NA direction ?

Can you predict when and where the next one should occur

NB : the San Andreas Fault takes only 35 mm/yr

out of 50 mm/yr imposed by the plate motion

You will make the hypothese of the seismic cycle

Exercice on the Seismic risk on the San Andreas Fault

The shear strain rates

Dx

v1 v2

yy = Shear strain rates

= Dvy/Dx

= (V1 –V2)/Dx

The deformation in the direction perpendicular to V

y

Draw a profile of the Shear Strain rate and conclude?

x

. .

Question

Define the maximun strain on the SAF assuming that 200 years separate two successive earthquakes.

Geometric interpretation ofshear strain rate

=change in angle

Dx

V1 v2

yy = Shear strain rates = tan()

y

x

. . .

Geometric interpretation ofnormal strain

?

(shortening or lengthening)

Geometric interpretation of normal strain

=Change in length

Dx

l1

l2

yy = normal strain = Dly /Dy

y

x

xx yx

xy yy

The Matrix notation

( )

NOTE

yx = xy

xx yy

( )

The strain matrix is symetric

Deformation of the vector P ?

xx

yy Matrix:

P = Px

Py P

The matrix product allow to resolve the components of the strain For a given direction P

xx

xx

That is Deformation of the vector P :

pxx Px + Py

Px + yy Py

Px

Py.P =

Along x

Along y

Exercices :deform the above square and

circle using the following strainssupposed uniform

xx = 0.5

yy = 2

xy = 0.5

yx = 0.5

xx = -0.5 and yy = 0.5 and

xy = -0.5 and yx = -0.5

xy = 2 and yx = 2

Displacement -

Velocities

Strain

-

Strain rates

To measure the rigid motion of the plates or

of individual points we use the concepts of :

To measure the deformation of the crust or of the lithosphere

we use the concepts of :

The math object associated is a vector

The math object associated is a matrix

REMEMBER

SouthCalifornia

San Andreas Big Bend San Andreas South

Parallel and

tangeantcomponents

of the plate

motion resolved on the 1) SAFand on the2) Big bend

The perpendicular component is associated with the creation of topography with inverse faults

IN MAP view

Lateral motion :

Strike-Slip Fault

Perpendicular motion :

Inverse Fault

Perpendicular motion :

Normal Fault

V

n

Resoling the tangeant and perpendicular component

• nXV=O

•Tangential slip rate t = n.V

Strike-Slip Fault

Perpendicular motion :

• n.V=0•perpendicular slip : e =p.V

Vn

n

np

The concept of Azimut to define the orientation of the plate

boundary in the horizontal plane

nNorth

Azimut

Horizontal plane

GPS velocities

Their Kinematic - motion

Divergent plate boundary condition in Atlantic

The segmentation of the mid oceanic ridge (MOR)