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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
The Pa-NA Boundary Zone
Tectonics
Motion of
Pa/NA
Fault SYSTEM
TOPOGRAPHY
The NAF offsets the geology features : 200km
The NAF Offsets mountain ranges
100 km
The NAF Offsets rivers : 100m – 1km
…m
200 m
200 m
200 m
200 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
100 km
(Reid 1910)
San Andreas
Big Bend
San Andreas south
South
California
Los 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 ?
Exercice on the Seismic risk on the San Andreas Fault
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
y
The shear strain rates
.
v2
v1
.
g = eyy = Shear strain rates
= Dvy/Dx
= (V1 –V2)/Dx
x
Dx
The deformation in the direction perpendicular to V
Draw a profile of the Shear Strain rate and conclude?
Question
Define the maximun strain on the SAF
assuming that 200 years separate two
successive earthquakes.
y
Geometric interpretation of
shear strain rate
=
change in angle
.
g = eyy = Shear strain rates = tan(a)
.
a
V1
x
v2
Dx
.
Geometric interpretation of
normal strain
?
(shortening or lengthening)
y
Geometric interpretation of
normal strain
=
Change in length
eyy = normal strain = Dly /Dy
l2
x
l1
Dx
The Matrix notation
 exx eyx
e= (
)
 exy eyy
NOTE
The strain matrix is symetric
 g = eyx = exy
 exx g
e= (
)
 g eyy
Deformation of the vector P ?
Matrix:
e=
exx g
g eyy
P = Px
Py
P
The matrix product allow to resolve
the components of the strain
For a given direction P
e.P=
exx g
g exx
Px
.
Py
That is Deformation of the vector P :
ep = exx Px + g Py
g Px + eyy Py
Along x
Along y
Exercices :
deform the above square and
circle using the following strains
supposed uniform
exx = 0.5
eyy = 2
exy = 0.5
eyx = 0.5
exy = -0.5 and eyx = -0.5
exx = -0.5 and eyy = 0.5 and
exy = 2 and eyx = 2
REMEMBER
To measure the rigid motion of the plates or
of individual points we use the concepts of :
Displacement
Velocities
The math object associated is a vector
To measure the deformation of the crust or of the lithosphere
we use the concepts of :
Strain
Strain rates
The math object associated is a matrix
South
California
Parallel and
tangeant
components
of the plate
motion resolved
on the
1) SAF
and on the
2) Big bend
San Andreas
Big Bend
San Andreas Sout
The perpendicular component is
associated with the creation of
topography with inverse faults
IN MAP view
V
n
Lateral motion :
Strike-Slip Fault
Perpendicular motion :
Inverse Fault
Perpendicular motion :
Normal Fault
Resoling the tangeant and
perpendicular component
n
V
n
• nXV=O
•Tangential slip rate t = n.V
Strike-Slip Fault
Perpendicular motion :
n
p
•
n.V=0
•perpendicular slip :
e =p.V
The concept of Azimut to define
the orientation of the plate
boundary in the horizontal plane
Azimut
North
n
Horizontal plane
GPS velocities
Their Kinematic - motion
Divergent plate boundary condition in
Atlantic
The segmentation of the mid
oceanic ridge (MOR)