Lecture 15 Strike-slip Faults

8/11/2019 Lecture 15 Strike-slip Faults

1/13

ENVS388

Lecture 15Elastic dislocation modelling:

Strike-slip faults


2/13

Modelling deformation due to slip on a fault

Elastic dislocation modelling is used to model deformation of the

crust resulting from slip on faults (e.g. earthquakes)

Assumptions:

Elastic, homogeneous Earth

Earth is flat

Fault slip is a displacement discontinuity across a plane - this isthe dislocation

Occasionally a layered Earth will be implemented

Rectangular dislocations are most common

Triangular dislocations may also be used


3/13

Elastic rebound theory

After the 1906 San Francisco earthquake,

Henry Reid formulated his theory ofelastic rebound. According to this theory,elastic strains build up during theinterseismic phase of an earthquake cycleand are released during the coseismicphase. Think of a fence post!

Fence offset that

occurred during the

1906 earthquake


4/13

Hedge offset that occurred during the 2010

Darfield earthquake, New Zealand

Railtrack offset that occurred

during the 2010 Baja earthquake,California

Offset of ploughed field that occurred during the

1979 Imperial Valley earthquake, California


5/13

Infinitely long vertical strike-slip fault (ILVSF)

An infinitely long strike-slip fault is the simplest scenario to model

There is an analytical solution for surface displacements (u) at distance xfrom the fault due to slip between depths d1and d2:

u =!s"

tan!1 x

d1

#

$%&

'(! tan!1

x

d2

#

$%&

'()

*+

,

-.

d1

d2

x

No displacement

discontinuity at thesurface since the fault

is buried

!50 !40 !30 !20 !10 0 10 20 30 40 50!30

!20

!10

0

10

20

30

distance (km)

displacemen

t(m)Since this case

considers an infinitelylong strike-slip fault,

surface displacements

are horizontal and

parallel to the fault.

(cm)


6/13

If the fault breaks the surface (d2!0), as frequently happens in earthquakes,then a special form of the general ILVSF expression can be derived.

First note that

End-member scenario (i) for ILVSF: coseismic case

limd2!0 tan

"1 x

d2

#

$%

&

'( =

)

2 sgn(x)

Now apply the trig identity tan!1 a( ) +tan!1 1

a

"#$ %&' =

(

2sgn(x)

which gives tan!1 x

d1

"

#$

%

&' +tan

!1 d1

x

"

#$

%

&' =

(

2

sgn(x)

and so

u =!s

"

tan!1 x

d1

#

$%

&

'(! tan

!1 x

d2

#

$%

&

'(

)

*+

,

-.GENERAL ILVSF EXPRESSION:

u =s

!

tan"1 d1

x

#$%

&'(

!50 !40 !30 !20 !10 0 10 20 30 40 50!

100

!50

0

50

100

distance (km)

displacement(m)

Now there is a

discontinuity atzero distance

x

(cm)


7/13

If the fault goes to infinite depth (d1!"), then another special form of thegeneral ILVSF expression can be derived.

Since

End-member scenario (ii) for ILSF: interseismic case

limd1!"

tan#1 x

d1

$

%&

'

() =0

the expression simply becomes

u =!s

"

tan!1 x

d1

#

$%

&

'(! tan

!1 x

d2

#

$%

&

'(

)

*+

,

-.GENERAL ILVSF EXPRESSION:

u =s

!

tan"1 x

d2

#

$%&

'(

x

locking depth

This arctan function is characteristic

of interseismic displacements. The

wavelength of the function is

related to the locking depth: deeper

locking depth gives a longer-

wavelength arctan curve. !50 !40 !30 !20 !10 0 10 20 30 40 50!80

!60

!40

!20

0

20

40

60

80

distance (km)

displacement(m)

(mm/yr)

Note that sis often slip rate,instead of just slip.


8/13

Elastic rebound theory revisited

The two end-member ILVSF expressions can be thought of as representing

the coseismic case (the earthquake itself) and the interseismic case (the slowbuild-up of strain in between earthquakes). Over a complete cycle (coseismic+ interseismic), the displacement at all distances should represent blockmotion - which is the basis of elastic rebound theory.

!50 !40 !30 !20 !10 0 10 20 30 40 50!100

!80

!60

!40!

20

0

20

40

60

80

100

distance (km)

displa

cement(m)

interseismic

coseismic

total


9/13

A finite but long strike-slip fault

! #$%&

'#%&

()*

(**

)* * )* (** ()*

+*

,*

-*

*

-*

,*

+*

.#/%&

()

(*

)

*

)

(*

()

For a long but finite strike-slip fault, a displacement profile through the centreof the fault is a close approximation to the infinitely long case, i.e.displacements are primarily horizontal and parallel to the fault. Note thatthere is also now a small amount of vertical displacement, particularly at theends of the fault.

MODEL

Y(km)


10/13

A real earthquake

The 2001 Manyi earthquake onthe Tibetan Plateau ruptured a

200 km-long left-lateral strike-slip fault.

The image on the right is acollage of three InSAR images(you can just see the diagonal

joins).

The blue and red curves in thelower figure show displacementsextracted from two of the

images along the black line.

The grey curve is thedisplacement modelled accordingto elastic dislocation theory.

The elastic model shows a veryclose fit to the observed

displacements.

Peltzer et al. (1999)


11/13

! #$%&

'#%&

() *) +) ,) -) ) -) ,) +) *) ()

()

*)

+)

,)

-)

)

-)

,)

+)

*)

()

.#/%&

,)

-(

-)

(

)

(

-)

-(

,)

Short strike-slip

faults

Shorter faults have more of a

rotational displacement field

MODEL

GPS displacements in

Canterbury, New Zealand

resulting from the 2010

Darfield earthquake

Note that for the Darfield earthquake,

as for strike-slip earthquakes in

general, horizontal displacements are

significantly larger than vertical

displacements.

Y(km)


12/13

A short, dipping strike-slip fault

While vertical strike-slipfaults result in symmetricaldisplacements either side

of the fault, a dipping faultintroduces someasymmetry into thedisplacement field. In thisexample, the fault isdipping 60 to the north.

! #$%&

'#$%&

() *) +) ,) -) ) -) ,) +) *) ()

()

*)

+)

,)

-)

)

-)

,)

+)

*)

()

.#/%&

0)

*)

,)

)

,)

*)

0)

MODEL


13/13

Wright et al. (2001)

Ryder & Brgmann (2008)

Interseismic strain accumulation

Interseismic

displacementsassociated withthe NorthAnatolian Faultover a 7-yearperiod. Thelocking depth ofthe fault is

estimated to be~18 km.

Interseismic

displacementsassociated with thecentral SanAndreas Fault.over a 9-yearperiod. The lockingdepth of the faultis estimated to be

a few kilometres.The fault istherefore classedas creeping.

Note the arctan-likemodel function

Note the much shorter wavelength of the arctan function

in the creeping fault case compared the locked case.

Lecture 15 Strike-slip Faults

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