Long Term Flexure of the Crust and Sismogenesis, Application to the San Andreas Fault (California)

Laetitia Le Pourhiet*, Evgenii Burov

Laboratoire de tectonique Univ. P. et M. Curie Paris 6laetitia.le_pourhiet@upmc.fr

Elastic Strength of the crust as A link Between Quakes and Geodynamics?The simplest rheological model for the crust in shear is:

visco - elasto - Brittle

Elastic Flexure Controls the orientation of joints

Elastic Strain are small, However OnLy Elasticity may store energyOver Long time scale...

And Therefore ... .... the fluid Path ways

T53C-1955Long Term Flexure of the Crust and Sismogenesis, Application to the San Andreas Fault (California)

ABSTRACT: However, flexure affects the orientation and magnitude of principal stresses acting within the continental crust. We try to highlight some quantitative and putative links between flexure, the me-chanical behavior of faults,their seismic activity at smaller time scale and to apply them to the well do-cumented San Andreas Fault. First impact of flexure is that it allows building differential stresses both at the surface and at the base of an elastic plate without loading it in the center.

0 1 2 3 4 51

1.5

2

2.5

3

3.5

4

4.5

5

shear strain %

maj

or p

rinci

pal s

tres

s ou

tsid

e

30°

2 1 0normal stress

3 2 1 00

0.5

1

1.5

22.5

5 4 3 2 1 0

1 00

0.5

1

normal stress

shea

r str

ess

Strength at yield Stregth after 5 % shear strain on the fault

Grgz

=100

shea

r str

ess

M.C. plasticity for preexiting faults

Faults and Quakes: A pseudo-static point of view

I Continuum mechanics applies. Faults have a thickness in which Morh Coulomb elastic-plastic rheology applies and diplacement on the interfaces between the fault and surrounding media is compatible shear and normal com-ponent of the stress on the fault plane are continuous, only the fault parallel stress component can be dicontinuous.

stable plastic creep

yL

x

y

σyy < σxx

x

Coulomb

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

μeff

εii %

0

2

4

-1

γxy %

μres

tan Ψ

L

x

y

L

x

yL

x

Roscoe

zone of possible slip instability

x

σ1

σ3

σyy > σxx

Byerlee friction is mesured at peak

However, asumimg continuity of stress there are many possible state possible inside the fault (red circle) Therefore, this effective friction does not tell anything about the strength of the fault (the radius of the red circle).

Fortunately, using a full rheological computation instead of solely a rupture criteria it is possible to get more informations

Inverting strain mesurements issued from borehole breakouts, earthquake focal mechanism or microfracture one can get a the orientation of principal stress axis in the surrounding of faults.

Comparing this orientation to the orientation of the fault one finds the effective friction of the fault.

well oriented fault (plain lines) : friction angle compa-tible with lab experiments allows for larger stress drop and favor slip instability.

very badly oriented fault (dashed lines) cause harde-ning and allow stable creep to occur only for effective friction approx. equal to the orientation vs. s1). For higher effective friction new fault form.

Stress is allowed to rotate within the shear band, depen-ding on the sense of rotation, the deviatoric stress in the surrounding elastic media will rise (hardening) or drop (softening)

Cited References Atwater T. & Stock J.M. - 1998 , Pacific–North America plate tectonics of the Neogene southwestern United States: an update, Int. Geol. Rev. 40 , pp. 375–402. Boyd et al - 2004; Foundering lithosphere imaged beneath the Southern Sierra Nevada, California, USA, Science 305 (5684), pp. 660–662.Hill et al. 1990; Seismicity 1980-1986 in The San Andreas fault system, California; USGS professional paper 1515 , p115-151Kwon Y.W. & Bang H.- 1997 The finite Element Method Using Matlab CRC press p 366-369Le Pourhiet et al. 2006; Mantle instability beneath the Sierra Nevada Mountains in California and Death Valley exten-sion; EPSL 251 p 104-119Leroy Y and Ortiz M -1989; Localization Analysis under Dynamic Loading; INST PHYS CONF SER (102): 257-265Rice J. 1992; Chapter 20: Fault stress state, pore pressure distribution and the weakness of the San andreas faults in fault mechanics and transport properties of rocks eds B. Evans& T-F Wong Academic press ltd- p476 -503Saleeby J and Foster Z. -2004 ; Topographic response to mantle lithosphere removal in the southern Sierra Nevada region, California Geology 32 p. 245-248Sibson R. -1990; rupture nucleation on unfavorably oriented faults; BSSA 80, pp. 1580-1604Sibson R. -2003Brittle-failure controls on maximum sustainable overpressure in different tectonic regimes , AAPG Bulle-tin, v. 87, pp. 901–908Townend and Zoback,- 2001 in The Nature and Tectonic Significance of Fault Zone Weakening R. E. Holdsworth, R. A. Strachan, J. F. Maglouhlin, J. F. Knipe, Eds. , vol. 186, pp. 13-21.Thurber C. et al.- 2006; Three dimensional speed model earthquake relocations and focal mechanisms for the Parkfield california region BSSA 96, pS38-S49Unruh J. , -1991; The uplift of the Sierra Nevada and implications for Late Cenozoic epeirogeny in the western Cordillera, Geol. Soc. Amer. Bull. 103 pp. 1395–1404.

10°

15°

Rice J. 1992Sibson R. -1990

Application to the San Adreas Fault

The San Andreas Fault is a system of dextral strike slip faults which runs from the Gulf of California (Mexico) to the Mendicino triple junction (Washington, USA). This plate boundary has been initiated 30 Myr ago as the ridge, which separated the Faralon plate from the Pacific plate, collided with the North American Plate (Atwater and Stokes 1998). The fault is segmented along strike and we are mainly interested with three segments which are located along the border of the Sierra Nevada micro-plate. In this area, the main fault is orthogonal to the regional maximum horizontal stress (Towend and Zoback 2001 ) and has there-fore been recognized as a weak fault . However, the apparent frictional weakness of the fault does not prevent big earthqua-kes such as the one which destroy San Fran-cisco in 1906 to occur In the middle of those two seismic segments, a 150 km long segment is creeping aseismically from Park-field to San Juan Bautista. A question arises from those observations: what factor con-trols the apparent contrasting behavior of the fault along strike.

QUAKES

150 KM

Hill et al 1990

Seismic tomography outlines the presence of a fast body sinking toward the east beneath the Great Valley

while

Reciever functions show that East of this ano-maly, the Moho has very weak signature. Both are interpreted as the signature of the re-moval of the ultra-mafic root of the Sierra Nevada Batholith.

Parkfield S.Creeping S. Cholame S. 1857 break

1966

20041984-2004

2004-2006

Lowest Point in the US

Highest point in the US

Convective Instability

Creeping segment

300 km

DRIPS

Boyd et al 2004

FLEXURE

Geomorphology coupled with stratigra-phy clearly indicate:

1 : A long term (5-10 Myr) flexural tilt of the Sierra Nevada micro-plate all along its axis

2 : A recent increase of the downward tilt at the level outlined by the red rectangle

The creeping segment is an 150km long band which concentrates a lot of seismicity at shallow (<12km) depths. It contrast with the size mean size of the body of ophilite in the Franciscan Complex. (see the ultra maphic body on the general map of california).

The seismic activity of this segment contrasts with its surrounding segments which rup-tured with destructive earthquakes ( Loma Prieta (1989), San Francisco (1906) and Carrizo Plain (1857)) .

126

°W

124

°W

122

°W

120

°W 1

18°W

34°

N

36°

N

38°

N

40°

N 4

2°N

SFSJB

3.5 cm/yr (vs SN)

GREAT VALLEY

a

a’

b

b’

Tulare

SIERRA NEVADA MOUNTAINS

SAF 1857

1906 SAF

Pkd

PAC

Eastern California Shear Zone

CMa0

Coast Ranges

Mantle Drip −140

−120

−100

−80

−60

−40

−20

0

Dep

th (k

m)

400600

800

1000

1200

Mantle S.N. BatholithCrustgranitecpx-gt root

Great ValleyBasin and Range

lithospheredepleted

S.N.SAF Coalinga

−50 0 50 100 150 200 250

a a’a0A

50MPa

-50MPaBending stressnormal to the SAF

comp.tens.

0

100

2000

100200

300400

500600

700

Dep

th

-100

SAF

km

km

kma

b

PkdSJB

σv σ1+Bσ1+Bσ3 σ1-Bσ1-B σ1σ1

σv ~ σ3 σv > σ3τ

σn

B

500 1000

M>33>M>22>M>11>M

0

5

10

15

N events

dept

h (k

m)

A B C

~8 km

a

a’ ESFS

b

b’

Drip pull

MODELING IT

A Coincidence OR Not ? The Facts...

Do We Observe That Somewhere ?

fau

lt c

ore

Dammage Zone

Elastic media

fau

lt c

ore

Dammage Zone

Elastic media

Elastic media

fau

lt c

ore

Dammage Zone

SticK-Slip

Fluid barrier

lithostatichydrostatic

water discharge

slow refilling of the reservoir

slow refilling of the reservoir

Fluid barrierreforms

slow refilling of the reservoir

t1t0 t2

tQ

tQ

t2

t1

t0

fluid pressure

II Although it is possible to trigger a slip instability in a hardening material under dynamic loading (i.e. during an earth quake, see Leroy and Ortiz 1989). There should be an initial zone (patch) in which slip instability occurs in the static regime to initiate an earthquake. Hence, the initiation of earthquake necessite some effec-tive strain softening.

III This initial strain softening cannot be related to a modification of the nominal/ lab friction of the material be-cause: a) it is reproducible (happend at each rupture) b) the amount of strain is small (otherwise there would be significant precursor to earthquakes)Hence, I favour structural softening effects over wear.

IV High fluid pressure, nearly lithostatic, may only be sustained if the sealing is in a compressive setting (Sibson 2003)

Effective Friction, stress inversions Mechanical Statements

τ

σn2θ

ΔPf

φfault=φB

τ

σn2θ

ΔPf =0

φBφfault=φeff

τ

σn2θ

ΔPf

φBφfault>φeff?

?

?

Localisation of the different modelsand observations

Results of the 2D Plane strain Thermo-mechanical Model

Results of 2D plane stress Modeldetermining flexural bending dueto convective instability

Parametric Study of the effect of coupling and plate thickness

Variation of jointing along the strike of the SAF causes the contrastingSeismic behavior from "aseismic" Creep to destructive Earth Quakes

Presented Model

As the state of stress Changes with depth favoring vertical joints in the extrado and horizontal joints in the intrado, the depth of formation of fluid barriers which help maintaining fluid over pressure up to lithostatic level, i.e. low effective strength, happens to be control by flexure. This Model seems to apply at least for strike slip faults like the San Andreas fault.

Sibson R. -2003

Thurber et al 2006

Saleeby et Foster 2004

Le Pourhiet et al 2006